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# Edit detail for RichExp2 revision 1 of 1

 1 Editor: test1 Time: 2015/06/15 16:49:59 GMT+0 Note:

changed:
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Examples involving exponential function from Albert Rich testsuite.

\begin{axiom}

)set messages time on
)set break resume
)set output tex off
)set output algebra on

-- Integrands of the form x^m F^(c (a+b x)^n)

-- n>0
integrate(f^(c*(a+b*x)^2)*x^m, x)
integrate(f^(c*(a+b*x)^2)*x^3, x)
integrate(f^(c*(a+b*x)^2)*x^2, x)
integrate(f^(c*(a+b*x)^2)*x, x)
integrate(f^(c*(a+b*x)^2), x)
integrate(f^(c*(a+b*x)^2)/x, x)
integrate(f^(c*(a+b*x)^2)/x^2, x)
integrate(f^(c*(a+b*x)^2)/x^3, x)
integrate(f^(c*(a+b*x)^3)*x^m, x)
integrate(f^(c*(a+b*x)^3)*x^2, x)
integrate(f^(c*(a+b*x)^3)*x, x)
integrate(f^(c*(a+b*x)^3), x)
integrate(f^(c*(a+b*x)^3)/x, x)
integrate(f^(c*(a+b*x)^3)/x^2, x)
integrate(f^(c*(a+b*x)^3)/x^3, x)
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^m, x)
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^4, x)
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^3, x)
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^2, x)
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x, x)
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3), x)
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)/x, x)
integrate(%e^sqrt(5+3*x), x)

-- n<0
integrate(f^(c/(a+b*x))*x^m, x)
integrate(f^(c/(a+b*x))*x^4, x)
integrate(f^(c/(a+b*x))*x^3, x)
integrate(f^(c/(a+b*x))*x^2, x)
integrate(f^(c/(a+b*x))*x, x)
integrate(f^(c/(a+b*x)), x)
integrate(f^(c/(a+b*x))/x, x)
integrate(f^(c/(a+b*x))/x^2, x)
integrate(f^(c/(a+b*x))/x^3, x)
integrate(f^(c/(a+b*x)^2)*x^m, x)
integrate(f^(c/(a+b*x)^2)*x^4, x)
integrate(f^(c/(a+b*x)^2)*x^3, x)
integrate(f^(c/(a+b*x)^2)*x^2, x)
integrate(f^(c/(a+b*x)^2)*x, x)
integrate(f^(c/(a+b*x)^2), x)
integrate(f^(c/(a+b*x)^2)/x, x)
integrate(f^(c/(a+b*x)^2)/x^2, x)
integrate(f^(c/(a+b*x)^2)/x^3, x)
integrate(f^(c/(a+b*x)^3)*x^m, x)
integrate(f^(c/(a+b*x)^3)*x^4, x)
integrate(f^(c/(a+b*x)^3)*x^3, x)
integrate(f^(c/(a+b*x)^3)*x^2, x)
integrate(f^(c/(a+b*x)^3)*x, x)
integrate(f^(c/(a+b*x)^3), x)
integrate(f^(c/(a+b*x)^3)/x, x)
integrate(f^(c/(a+b*x)^3)/x^2, x)
integrate(f^(c/(a+b*x)^3)/x^3, x)

-- n symbolic
integrate(f^(c*(a+b*x)^n)*x^m, x)
integrate(f^(c*(a+b*x)^n)*x^3, x)
integrate(f^(c*(a+b*x)^n)*x^2, x)
integrate(f^(c*(a+b*x)^n)*x, x)
integrate(f^(c*(a+b*x)^n), x)
integrate(f^(c*(a+b*x)^n)/x, x)
integrate(f^(c*(a+b*x)^n)/x^2, x)
integrate(f^(c*(a+b*x)^n)/x^3, x)

-- Integrands of the form (c+d x)^m F^(a+b (c+d x)^n)

-- n>0
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^m, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^11, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^9, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^7, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^5, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^3, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x), x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x), x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^3, x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^5, x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^7, x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^9, x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^11, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^12, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^10, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^8, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^6, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^4, x)
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^2, x)
integrate(F^(a+b*(c+d*x)^2), x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^2, x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^4, x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^6, x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^8, x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^10, x)
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^12, x)
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^m, x)
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^17, x)
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^14, x)
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^11, x)
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^8, x)
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^5, x)
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^2, x)
integrate(F^(a+b*(c+d*x)^3)/(c+d*x), x)
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^4, x)
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^7, x)
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^10, x)
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^13, x)
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^16, x)
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^3, x)
integrate(F^(a+b*(c+d*x)^3)*(c+d*x), x)
integrate(F^(a+b*(c+d*x)^3), x)
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^2, x)
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^3, x)
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^5, x)
integrate(f^(a+b*(c+d*x)^(1/2)), x)
integrate(f^(a+b*(c+d*x)^(1/3)), x)

-- n<0
integrate(F^(a+b/(c+d*x))*(c+d*x)^m, x)
integrate(F^(a+b/(c+d*x))*(c+d*x)^4, x)
integrate(F^(a+b/(c+d*x))*(c+d*x)^3, x)
integrate(F^(a+b/(c+d*x))*(c+d*x)^2, x)
integrate(F^(a+b/(c+d*x))*(c+d*x), x)
integrate(F^(a+b/(c+d*x)), x)
integrate(F^(a+b/(c+d*x))/(c+d*x), x)
integrate(F^(a+b/(c+d*x))/(c+d*x)^2, x)
integrate(F^(a+b/(c+d*x))/(c+d*x)^3, x)
integrate(F^(a+b/(c+d*x))/(c+d*x)^4, x)
integrate(F^(a+b/(c+d*x))/(c+d*x)^5, x)
integrate(F^(a+b/(c+d*x))/(c+d*x)^6, x)
integrate(F^(a+b/(c+d*x))/(c+d*x)^7, x)
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^m, x)
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^9, x)
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^7, x)
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^5, x)
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^3, x)
integrate(F^(a+b/(c+d*x)^2)*(c+d*x), x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x), x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^3, x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^5, x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^7, x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^9, x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^11, x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^13, x)
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^10, x)
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^8, x)
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^6, x)
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^4, x)
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^2, x)
integrate(F^(a+b/(c+d*x)^2), x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^2, x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^4, x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^6, x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^8, x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^10, x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^12, x)
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^14, x)
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^m, x)
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^14, x)
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^11, x)
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^8, x)
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^5, x)
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^2, x)
integrate(F^(a+b/(c+d*x)^3)/(c+d*x), x)
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^4, x)
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^7, x)
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^10, x)
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^13, x)
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^16, x)
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^19, x)
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^3, x)
integrate(F^(a+b/(c+d*x)^3)*(c+d*x), x)
integrate(F^(a+b/(c+d*x)^3), x)
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^2, x)
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^3, x)
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^5, x)

-- n symbolic
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^m, x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^3, x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^2, x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x), x)
integrate(F^(a+b*(c+d*x)^n), x)
integrate(F^(a+b*(c+d*x)^n)/(c+d*x), x)
integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^2, x)
integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^3, x)
integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^4, x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+6*n), x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+5*n), x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+4*n), x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+3*n), x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+2*n), x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+n), x)
integrate(F^(a+b*(c+d*x)^n)/(c+d*x), x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-n), x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-2*n), x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-3*n), x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-4*n), x)
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-5*n), x)
integrate(F^(c*(a+b*x)^n)*(a+b*x)^(-1+1/2*n), x)
integrate((a+b*x)^(-1+1/2*n)/F^(c*(a+b*x)^n), x)

-- Integrands of the form (e+f x)^m F^(a+b (c+d x)^n)

-- n>0
integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^5, x)
integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^4, x)
integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^3, x)
integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^2, x)
integrate(F^(a+b*(c+d*x)^2)*(e+f*x), x)
integrate(F^(a+b*(c+d*x)^2), x)
integrate(F^(a+b*(c+d*x)^2)/(e+f*x), x)
integrate(F^(a+b*(c+d*x)^2)/(e+f*x)^2, x)
integrate(F^(a+b*(c+d*x)^2)/(e+f*x)^3, x)
integrate(%e^(e*(c+d*x)^3)*(a+b*x)^3, x)
integrate(%e^(e*(c+d*x)^3)*(a+b*x)^2, x)
integrate(%e^(e*(c+d*x)^3)*(a+b*x), x)
integrate(%e^(e*(c+d*x)^3), x)
integrate(%e^(e*(c+d*x)^3)/(a+b*x), x)
integrate(%e^(e*(c+d*x)^3)/(a+b*x)^2, x)

-- n<0
integrate(F^(a+b/(c+d*x))/(e+f*x), x)
integrate(F^(a+b/(c+d*x))/(e+f*x)^2, x)
integrate(F^(a+b/(c+d*x))/(e+f*x)^3, x)
integrate(F^(a+b/(c+d*x))/(e+f*x)^4, x)
integrate(%e^(e/(c+d*x))*(a+b*x)^4, x)
integrate(%e^(e/(c+d*x))*(a+b*x)^3, x)
integrate(%e^(e/(c+d*x))*(a+b*x)^2, x)
integrate(%e^(e/(c+d*x))*(a+b*x), x)
integrate(%e^(e/(c+d*x)), x)
integrate(%e^(e/(c+d*x))/(a+b*x), x)
integrate(%e^(e/(c+d*x))/(a+b*x)^2, x)
integrate(%e^(e/(c+d*x))/(a+b*x)^3, x)
integrate(%e^(e/(c+d*x)^2)*(a+b*x)^3, x)
integrate(%e^(e/(c+d*x)^2)*(a+b*x)^2, x)
integrate(%e^(e/(c+d*x)^2)*(a+b*x), x)
integrate(%e^(e/(c+d*x)^2), x)
integrate(%e^(e/(c+d*x)^2)/(a+b*x), x)
integrate(%e^(e/(c+d*x)^2)/(a+b*x)^2, x)
integrate(%e^(e/(c+d*x)^2)/(a+b*x)^3, x)
integrate(%e^(e/(c+d*x)^3)*(a+b*x)^3, x)
integrate(%e^(e/(c+d*x)^3)*(a+b*x)^2, x)
integrate(%e^(e/(c+d*x)^3)*(a+b*x), x)
integrate(%e^(e/(c+d*x)^3), x)
integrate(%e^(e/(c+d*x)^3)/(a+b*x), x)
integrate(%e^(e/(c+d*x)^3)/(a+b*x)^2, x)
\end{axiom}


Examples involving exponential function from Albert Rich testsuite.

fricas
)set messages time on

fricas
)set break resume

fricas
)set output tex off

fricas
)set output algebra on
-- Integrands of the form x^m F^(c (a+b x)^n)
-- n>0
integrate(f^(c*(a+b*x)^2)*x^m, x)
x        2 2               2
++    m (%A b  + 2 %A a b + a )c
(1)   |   %A f                        d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.01 (EV) + 0.19 (OT) = 0.21 sec
integrate(f^(c*(a+b*x)^2)*x^3, x)
(2)
+------------+
|   2
3   2      2                   +---+    (b x + a)\|- b c log(f)
(- 2 a b c log(f)  + 3 a b c log(f))\|%pi erf(------------------------)
b
+
2   2                  2
((2 b c x  - 2 a b c x + 2 a c)log(f) - 2)
*
2   2                2         +------------+
(b c x  + 2 a b c x + a c)log(f) |   2
%e                                \|- b c log(f)
/
+------------+
4 2      2 |   2
4 b c log(f) \|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(c*(a+b*x)^2)*x^2, x)
(3)
+------------+
|   2
2                +---+    (b x + a)\|- b c log(f)
(2 a b c log(f) - b)\|%pi erf(------------------------)
b
+
2   2                2         +------------+
(b c x  + 2 a b c x + a c)log(f) |   2
(2 b x - 2 a)%e                                \|- b c log(f)
/
+------------+
3         |   2
4 b c log(f)\|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^2)*x, x)
(4)
+------------+
|   2
+---+    (b x + a)\|- b c log(f)
- a b c log(f)\|%pi erf(------------------------)
b
+
2   2                2         +------------+
(b c x  + 2 a b c x + a c)log(f) |   2
%e                                \|- b c log(f)
/
+------------+
2         |   2
2 b c log(f)\|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^2), x)
+------------+
|   2
+---+    (b x + a)\|- b c log(f)
\|%pi erf(------------------------)
b
(5)  -----------------------------------
+------------+
|   2
2 \|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^2)/x, x)
2 2               2
x  (%A b  + 2 %A a b + a )c
++  f
(6)   |   ------------------------- d%A
++               %A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^2)/x^2, x)
2 2               2
x  (%A b  + 2 %A a b + a )c
++  f
(7)   |   ------------------------- d%A
++                2
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^2)/x^3, x)
2 2               2
x  (%A b  + 2 %A a b + a )c
++  f
(8)   |   ------------------------- d%A
++                3
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^3)*x^m, x)
x        3 3       2   2         2     3
++    m (%A b  + 3 %A a b  + 3 %A a b + a )c
(9)   |   %A f                                    d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^3)*x^2, x)
(10)
3   3        2   2      2         3          +------------+2
(b c x  + 3 a b c x  + 3 a b c x + a c)log(f) 3|   3
%e                                              \|- b c log(f)
+
-
2                1     3   3        2   2      2         3
a b c log(f)Gamma(-,(- b c x  - 3 a b c x  - 3 a b c x - a c)log(f))
3
*
+------------+
3|   3
\|- b c log(f)
+
2              2     3   3        2   2      2         3
2 a b c log(f)Gamma(-,(- b c x  - 3 a b c x  - 3 a b c x - a c)log(f))
3
/
+------------+2
3        3|   3
3 b c log(f)\|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^3)*x, x)
(11)
+------------+
1     3   3        2   2      2         3         3|   3
a Gamma(-,(- b c x  - 3 a b c x  - 3 a b c x - a c)log(f))\|- b c log(f)
3
+
2     3   3        2   2      2         3
- b Gamma(-,(- b c x  - 3 a b c x  - 3 a b c x - a c)log(f))
3
/
+------------+2
3|   3
3 b \|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^3), x)
1     3   3        2   2      2         3
Gamma(-,(- b c x  - 3 a b c x  - 3 a b c x - a c)log(f))
3
(12)  - --------------------------------------------------------
+------------+
3|   3
3 \|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^3)/x, x)
3 3       2   2         2     3
x  (%A b  + 3 %A a b  + 3 %A a b + a )c
++  f
(13)   |   ------------------------------------- d%A
++                     %A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^3)/x^2, x)
3 3       2   2         2     3
x  (%A b  + 3 %A a b  + 3 %A a b + a )c
++  f
(14)   |   ------------------------------------- d%A
++                      2
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^3)/x^3, x)
3 3       2   2         2     3
x  (%A b  + 3 %A a b  + 3 %A a b + a )c
++  f
(15)   |   ------------------------------------- d%A
++                      3
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^m, x)
x     3 3       2   2         2     3
++    %A b  + 3 %A a b  + 3 %A a b + a   m
(16)   |   %e                                 %A d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^4, x)
(17)
3 3        2 2      2       3  +----+2
2 2                2   b x  + 3 a b x  + 3 a b x + a  3|   3
(3 b x  - 6 a b x + 9 a )%e                               \|- b
+
+----+
4               1    3 3        2 2      2       3 3|   3
(- 3 a  - 4 a)b Gamma(-,- b x  - 3 a b x  - 3 a b x - a )\|- b
3
+
3      2      2    3 3        2 2      2       3
(12 a  + 2)b Gamma(-,- b x  - 3 a b x  - 3 a b x - a )
3
/
+----+2
5 3|   3
9 b  \|- b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^3, x)
(18)
3 3        2 2      2       3  +----+2
b x  + 3 a b x  + 3 a b x + a  3|   3
(3 b x - 6 a)%e                               \|- b
+
+----+
3             1    3 3        2 2      2       3 3|   3
(3 a  + 1)b Gamma(-,- b x  - 3 a b x  - 3 a b x - a )\|- b
3
+
2 2      2    3 3        2 2      2       3
- 9 a b Gamma(-,- b x  - 3 a b x  - 3 a b x - a )
3
/
+----+2
4 3|   3
9 b  \|- b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^2, x)
(19)
3 3        2 2      2       3  +----+2
b x  + 3 a b x  + 3 a b x + a  3|   3
%e                               \|- b
+
+----+
2        1    3 3        2 2      2       3 3|   3
- a b Gamma(-,- b x  - 3 a b x  - 3 a b x - a )\|- b
3
+
2      2    3 3        2 2      2       3
2 a b Gamma(-,- b x  - 3 a b x  - 3 a b x - a )
3
/
+----+2
3 3|   3
3 b  \|- b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x, x)
(20)
+----+
1    3 3        2 2      2       3 3|   3
a Gamma(-,- b x  - 3 a b x  - 3 a b x - a )\|- b
3
+
2    3 3        2 2      2       3
- b Gamma(-,- b x  - 3 a b x  - 3 a b x - a )
3
/
+----+2
3|   3
3 b \|- b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3), x)
1    3 3        2 2      2       3
Gamma(-,- b x  - 3 a b x  - 3 a b x - a )
3
(21)  - -----------------------------------------
+----+
3|   3
3 \|- b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)/x, x)
3 3       2   2         2     3
x   %A b  + 3 %A a b  + 3 %A a b + a
++  %e
(22)   |   ----------------------------------- d%A
++                    %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^sqrt(5+3*x), x)
+-------+
+-------+       \|3 x + 5
(2 \|3 x + 5  - 2)%e
(23)  ------------------------------
3
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- n<0
integrate(f^(c/(a+b*x))*x^m, x)
c
x     --------
++    m %A b + a
(24)   |   %A f        d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.01 (EV) = 0.02 sec
integrate(f^(c/(a+b*x))*x^4, x)
(25)
4       4       4     2 3 2           3        2 3       3
(b c x + a c )log(f)  + (b c x  - 18 a b c x - 19 a c )log(f)
+
3 2 3         2 2 2       2   2         3 2       2
(2 b c x  - 14 a b c x  + 86 a b c x + 102 a c )log(f)
+
4   4         3   3       2 2   2       3             4
(6 b c x  - 16 a b c x  + 36 a b c x  - 96 a b c x - 154 a c)log(f)
+
5 5       5
24 b x  + 24 a
*
c log(f)
--------
b x + a
%e
+
5      5         4      4        2 3      3        3 2      2
- c log(f)  + 20 a c log(f)  - 120 a c log(f)  + 240 a c log(f)
+
4
- 120 a c log(f)
*
c log(f)
Ei(--------)
b x + a
/
5
120 b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x))*x^3, x)
(26)
3       3       3     2 2 2           2        2 2       2
(b c x + a c )log(f)  + (b c x  - 10 a b c x - 11 a c )log(f)
+
3   3        2   2       2            3              4 4      4
(2 b c x  - 6 a b c x  + 18 a b c x + 26 a c)log(f) + 6 b x  - 6 a
*
c log(f)
--------
b x + a
%e
+
4      4         3      3       2 2      2       3            c log(f)
(- c log(f)  + 12 a c log(f)  - 36 a c log(f)  + 24 a c log(f))Ei(--------)
b x + a
/
4
24 b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x))*x^2, x)
(27)
2       2       2     2   2                  2              3 3
(b c x + a c )log(f)  + (b c x  - 4 a b c x - 5 a c)log(f) + 2 b x
+
3
2 a
*
c log(f)
--------
b x + a
%e
+
3      3        2      2      2            c log(f)
(- c log(f)  + 6 a c log(f)  - 6 a c log(f))Ei(--------)
b x + a
/
3
6 b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x))*x, x)
(28)
c log(f)
--------
2 2    2    b x + a
((b c x + a c)log(f) + b x  - a )%e
+
2      2                   c log(f)
(- c log(f)  + 2 a c log(f))Ei(--------)
b x + a
/
2
2 b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x)), x)
c log(f)
--------
b x + a              c log(f)
(b x + a)%e         - c log(f)Ei(--------)
b x + a
(29)  ------------------------------------------
b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x))/x, x)
c log(f)
--------
b c x log(f)       a         c log(f)
(30)  Ei(- ------------)%e         - Ei(--------)
2                   b x + a
a b x + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x))/x^2, x)
c log(f)                   c log(f)
--------                   --------
b c x log(f)       a                  2    b x + a
- b c x log(f)Ei(- ------------)%e         + (- a b x - a )%e
2
a b x + a
(31)  ---------------------------------------------------------------------
2
a x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x))/x^3, x)
(32)
c log(f)
--------
2 2 2      2        2   2            b c x log(f)       a
(b c x log(f)  + 2 a b c x log(f))Ei(- ------------)%e
2
a b x + a
+
c log(f)
--------
2   2    2                2 2 2    4    b x + a
((a b c x  + a b c x)log(f) + a b x  - a )%e
/
4 2
2 a x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x)^2)*x^m, x)
c
---------------------
x       2 2               2
++    m %A b  + 2 %A a b + a
(33)   |   %A f                     d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^2)*x^4, x)
(34)
+----------+
|  c log(f)
b |- --------
|      2
3      3       2 2      2       4          +---+     \|     b
(- 4 c log(f)  - 60 a c log(f)  - 15 a c log(f))\|%pi erf(--------------)
b x + a
+
2 2           2       2
(4 b c x + 4 a b c )log(f)
+
4   3        3   2       2 2          3                6 5
(2 b c x  - 9 a b c x  + 36 a b c x + 47 a b c)log(f) + 3 b x
+
5
3 a b
*
c log(f)
-------------------
2 2              2
b x  + 2 a b x + a
%e
+
2      2       3                    c log(f)
(15 a b c log(f)  + 30 a b c log(f))Ei(-------------------)
2 2              2
b x  + 2 a b x + a
*
+----------+
|  c log(f)
|- --------
|      2
\|     b
/
+----------+
6 |  c log(f)
15 b  |- --------
|      2
\|     b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^2)*x^3, x)
(35)
+----------+
|  c log(f)
b |- --------
|      2
2      2      3          +---+     \|     b
(8 a c log(f)  + 4 a c log(f))\|%pi erf(--------------)
b x + a
+
3   2        2         2              5 4    4
((b c x  - 6 a b c x - 7 a b c)log(f) + b x  - a b)
*
c log(f)
-------------------
2 2              2
b x  + 2 a b x + a
%e
+
2      2      2                    c log(f)
(- b c log(f)  - 6 a b c log(f))Ei(-------------------)
2 2              2
b x  + 2 a b x + a
*
+----------+
|  c log(f)
|- --------
|      2
\|     b
/
+----------+
5 |  c log(f)
4 b  |- --------
|      2
\|     b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^2)*x^2, x)
(36)
+----------+
|  c log(f)
b |- --------
|      2
2      2      2          +---+     \|     b
(- 2 c log(f)  - 3 a c log(f))\|%pi erf(--------------)
b x + a
+
c log(f)
-------------------
2 2              2
2                        4 3    3    b x  + 2 a b x + a
((2 b c x + 2 a b c)log(f) + b x  + a b)%e
+
c log(f)
3 a b c log(f)Ei(-------------------)
2 2              2
b x  + 2 a b x + a
*
+----------+
|  c log(f)
|- --------
|      2
\|     b
/
+----------+
4 |  c log(f)
3 b  |- --------
|      2
\|     b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^2)*x, x)
(37)
+----------+
|  c log(f)
b |- --------
|      2
+---+     \|     b
2 a c log(f)\|%pi erf(--------------)
b x + a
+
c log(f)
-------------------
2 2              2
3 2    2    b x  + 2 a b x + a                       c log(f)
((b x  - a b)%e                    - b c log(f)Ei(-------------------))
2 2              2
b x  + 2 a b x + a
*
+----------+
|  c log(f)
|- --------
|      2
\|     b
/
+----------+
3 |  c log(f)
2 b  |- --------
|      2
\|     b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x)^2), x)
(38)
+----------+
|  c log(f)
b |- --------
|      2
+---+     \|     b
- c log(f)\|%pi erf(--------------)
b x + a
+
c log(f)
-------------------
2 2              2 +----------+
2          b x  + 2 a b x + a  |  c log(f)
(b x + a b)%e                    |- --------
|      2
\|     b
/
+----------+
2 |  c log(f)
b  |- --------
|      2
\|     b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^2)/x, x)
c
---------------------
2 2               2
x  %A b  + 2 %A a b + a
++  f
(39)   |   ---------------------- d%A
++             %A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x)^2)/x^2, x)
c
---------------------
2 2               2
x  %A b  + 2 %A a b + a
++  f
(40)   |   ---------------------- d%A
++               2
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^2)/x^3, x)
c
---------------------
2 2               2
x  %A b  + 2 %A a b + a
++  f
(41)   |   ---------------------- d%A
++               3
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^3)*x^m, x)
c
---------------------------------
x       3 3       2   2         2     3
++    m %A b  + 3 %A a b  + 3 %A a b + a
(42)   |   %A f                                 d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(f^(c/(a+b*x)^3)*x^4, x)
(43)
4   2         3          2 2              7 5      5 2
((3 b c x  - 24 a b c x - 27 a b c)log(f) + 2 b x  + 2 a b )
*
c log(f)
------------------------------
3 3        2 2      2       3
b x  + 3 a b x  + 3 a b x + a
%e
+
2 2                      c log(f)
- 20 a b c log(f)Ei(------------------------------)
3 3        2 2      2       3
b x  + 3 a b x  + 3 a b x + a
*
+----------+2
|  c log(f)
|- --------
3|      3
\|     b
+
2      2       3
(3 b c log(f)  - 20 a b c log(f))
*
+----------+
1              c log(f)              |  c log(f)
Gamma(-,- ------------------------------)  |- --------
3    3 3        2 2      2       3  3|      3
b x  + 3 a b x  + 3 a b x + a   \|     b
+
2      2       4               2              c log(f)
(- 30 a c log(f)  + 10 a c log(f))Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
b x  + 3 a b x  + 3 a b x + a
/
+----------+2
7  |  c log(f)
10 b   |- --------
3|      3
\|     b
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(f^(c/(a+b*x)^3)*x^3, x)
(44)
3           2            6 4    4 2
((3 b c x + 3 a b c)log(f) + b x  - a b )
*
c log(f)
------------------------------
3 3        2 2      2       3
b x  + 3 a b x  + 3 a b x + a
%e
+
2                      c log(f)
4 a b c log(f)Ei(------------------------------)
3 3        2 2      2       3
b x  + 3 a b x  + 3 a b x + a
*
+----------+2
|  c log(f)
|- --------
3|      3
\|     b
+
+----------+
2                1              c log(f)              |  c log(f)
6 a b c log(f)Gamma(-,- ------------------------------)  |- --------
3    3 3        2 2      2       3  3|      3
b x  + 3 a b x  + 3 a b x + a   \|     b
+
2      2      3               2              c log(f)
(3 c log(f)  - 4 a c log(f))Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
b x  + 3 a b x  + 3 a b x + a
/
+----------+2
6  |  c log(f)
4 b   |- --------
3|      3
\|     b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^3)*x^2, x)
(45)
c log(f)
------------------------------
3 3        2 2      2       3
5 3    3 2   b x  + 3 a b x  + 3 a b x + a
(b x  + a b )%e
+
2                      c log(f)
- b c log(f)Ei(------------------------------)
3 3        2 2      2       3
b x  + 3 a b x  + 3 a b x + a
*
+----------+2
|  c log(f)
|- --------
3|      3
\|     b
+
+----------+
1              c log(f)              |  c log(f)
- 3 a b c log(f)Gamma(-,- ------------------------------)  |- --------
3    3 3        2 2      2       3  3|      3
b x  + 3 a b x  + 3 a b x + a   \|     b
+
2              2              c log(f)
3 a c log(f)Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
b x  + 3 a b x  + 3 a b x + a
/
+----------+2
5  |  c log(f)
3 b   |- --------
3|      3
\|     b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.04 (EV) = 0.05 sec
integrate(f^(c/(a+b*x)^3)*x, x)
(46)
c log(f)
------------------------------
3 3        2 2      2       3  +----------+2
4 2    2 2   b x  + 3 a b x  + 3 a b x + a   |  c log(f)
(b x  - a b )%e                                |- --------
3|      3
\|     b
+
+----------+
1              c log(f)              |  c log(f)
b c log(f)Gamma(-,- ------------------------------)  |- --------
3    3 3        2 2      2       3  3|      3
b x  + 3 a b x  + 3 a b x + a   \|     b
+
2              c log(f)
- 2 a c log(f)Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
b x  + 3 a b x  + 3 a b x + a
/
+----------+2
4  |  c log(f)
2 b   |- --------
3|      3
\|     b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^3), x)
(47)
c log(f)
------------------------------
3 3        2 2      2       3  +----------+2
3       2   b x  + 3 a b x  + 3 a b x + a   |  c log(f)
(b x + a b )%e                                |- --------
3|      3
\|     b
+
2              c log(f)
c log(f)Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
b x  + 3 a b x  + 3 a b x + a
/
+----------+2
3  |  c log(f)
b   |- --------
3|      3
\|     b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^3)/x, x)
c
---------------------------------
3 3       2   2         2     3
x  %A b  + 3 %A a b  + 3 %A a b + a
++  f
(48)   |   ---------------------------------- d%A
++                   %A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x)^3)/x^2, x)
c
---------------------------------
3 3       2   2         2     3
x  %A b  + 3 %A a b  + 3 %A a b + a
++  f
(49)   |   ---------------------------------- d%A
++                     2
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^3)/x^3, x)
c
---------------------------------
3 3       2   2         2     3
x  %A b  + 3 %A a b  + 3 %A a b + a
++  f
(50)   |   ---------------------------------- d%A
++                     3
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
-- n symbolic
integrate(f^(c*(a+b*x)^n)*x^m, x)
x                 n
++    m c (%A b + a)
(51)   |   %A f             d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^n)*x^3, x)
x                 n
++    3 c (%A b + a)
(52)   |   %A f             d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^n)*x^2, x)
x                 n
++    2 c (%A b + a)
(53)   |   %A f             d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^n)*x, x)
x                 n
++      c (%A b + a)
(54)   |   %A f             d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^n), x)
x              n
++   c (%A b + a)
(55)   |   f             d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^n)/x, x)
n
x  c (%A b + a)
++  f
(56)   |   -------------- d%A
++         %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^n)/x^2, x)
n
x  c (%A b + a)
++  f
(57)   |   -------------- d%A
++           2
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^n)/x^3, x)
n
x  c (%A b + a)
++  f
(58)   |   -------------- d%A
++           3
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- Integrands of the form (c+d x)^m F^(a+b (c+d x)^n)
-- n>0
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^m, x)
(59)
m + 1       2 2                  2
Gamma(-----,(- b d x  - 2 b c d x - b c )log(F))
2
*
(- m + 1)log(- b log(F)) + 2 a log(F)
-------------------------------------
2
%e
/
2 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^11, x)
(60)
5 10 10       5   9 9       5 2 8 8        5 3 7 7        5 4 6 6
b d  x   + 10 b c d x  + 45 b c d x  + 120 b c d x  + 210 b c d x
+
5 5 5 5        5 6 4 4        5 7 3 3       5 8 2 2
252 b c d x  + 210 b c d x  + 120 b c d x  + 45 b c d x
+
5 9       5 10
10 b c d x + b c
*
5
log(F)
+
4 8 8       4   7 7        4 2 6 6        4 3 5 5
- 5 b d x  - 40 b c d x  - 140 b c d x  - 280 b c d x
+
4 4 4 4        4 5 3 3        4 6 2 2       4 7         4 8
- 350 b c d x  - 280 b c d x  - 140 b c d x  - 40 b c d x - 5 b c
*
4
log(F)
+
3 6 6        3   5 5        3 2 4 4        3 3 3 3
20 b d x  + 120 b c d x  + 300 b c d x  + 400 b c d x
+
3 4 2 2        3 5          3 6
300 b c d x  + 120 b c d x + 20 b c
*
3
log(F)
+
2 4 4        2   3 3        2 2 2 2        2 3          2 4
(- 60 b d x  - 240 b c d x  - 360 b c d x  - 240 b c d x - 60 b c )
*
2
log(F)
+
2 2                        2
(120 b d x  + 240 b c d x + 120 b c )log(F) - 120
*
2 2                  2
(b d x  + 2 b c d x + b c  + a)log(F)
%e
/
6        6
2 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^9, x)
(61)
4 8 8      4   7 7       4 2 6 6       4 3 5 5       4 4 4 4
b d x  + 8 b c d x  + 28 b c d x  + 56 b c d x  + 70 b c d x
+
4 5 3 3       4 6 2 2      4 7       4 8
56 b c d x  + 28 b c d x  + 8 b c d x + b c
*
4
log(F)
+
3 6 6       3   5 5       3 2 4 4       3 3 3 3       3 4 2 2
- 4 b d x  - 24 b c d x  - 60 b c d x  - 80 b c d x  - 60 b c d x
+
3 5         3 6
- 24 b c d x - 4 b c
*
3
log(F)
+
2 4 4       2   3 3       2 2 2 2       2 3          2 4       2
(12 b d x  + 48 b c d x  + 72 b c d x  + 48 b c d x + 12 b c )log(F)
+
2 2                      2
(- 24 b d x  - 48 b c d x - 24 b c )log(F) + 24
*
2 2                  2
(b d x  + 2 b c d x + b c  + a)log(F)
%e
/
5        5
2 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^7, x)
(62)
3 6 6      3   5 5       3 2 4 4       3 3 3 3       3 4 2 2
b d x  + 6 b c d x  + 15 b c d x  + 20 b c d x  + 15 b c d x
+
3 5       3 6
6 b c d x + b c
*
3
log(F)
+
2 4 4       2   3 3       2 2 2 2       2 3         2 4       2
(- 3 b d x  - 12 b c d x  - 18 b c d x  - 12 b c d x - 3 b c )log(F)
+
2 2                     2
(6 b d x  + 12 b c d x + 6 b c )log(F) - 6
*
2 2                  2
(b d x  + 2 b c d x + b c  + a)log(F)
%e
/
4        4
2 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^5, x)
(63)
2 4 4      2   3 3      2 2 2 2      2 3       2 4       2
(b d x  + 4 b c d x  + 6 b c d x  + 4 b c d x + b c )log(F)
+
2 2                    2
(- 2 b d x  - 4 b c d x - 2 b c )log(F) + 2
*
2 2                  2
(b d x  + 2 b c d x + b c  + a)log(F)
%e
/
3        3
2 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^3, x)
(64)
2 2                  2
((b d x  + 2 b c d x + b c )log(F) - 1)
*
2 2                  2
(b d x  + 2 b c d x + b c  + a)log(F)
%e
/
2        2
2 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x), x)
2 2                  2
(b d x  + 2 b c d x + b c  + a)log(F)
%e
(65)  ---------------------------------------
2 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x), x)
2 2                  2          a log(F)
Ei((b d x  + 2 b c d x + b c )log(F))%e
(66)  -----------------------------------------------
2 d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^3, x)
(67)
2 2                  2
(b d x  + 2 b c d x + b c  + a)log(F)
- %e
+
2 2                  2              2 2                  2
(b d x  + 2 b c d x + b c )log(F)Ei((b d x  + 2 b c d x + b c )log(F))
*
a log(F)
%e
/
3 2        2       2
2 d x  + 4 c d x + 2 c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^5, x)
(68)
2 2                  2
((- b d x  - 2 b c d x - b c )log(F) - 1)
*
2 2                  2
(b d x  + 2 b c d x + b c  + a)log(F)
%e
+
2 4 4      2   3 3      2 2 2 2      2 3       2 4       2
(b d x  + 4 b c d x  + 6 b c d x  + 4 b c d x + b c )log(F)
*
2 2                  2          a log(F)
Ei((b d x  + 2 b c d x + b c )log(F))%e
/
5 4         4 3       2 3 2       3 2       4
4 d x  + 16 c d x  + 24 c d x  + 16 c d x + 4 c d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^7, x)
(69)
2 4 4      2   3 3      2 2 2 2      2 3       2 4       2
(- b d x  - 4 b c d x  - 6 b c d x  - 4 b c d x - b c )log(F)
+
2 2                  2
(- b d x  - 2 b c d x - b c )log(F) - 2
*
2 2                  2
(b d x  + 2 b c d x + b c  + a)log(F)
%e
+
3 6 6      3   5 5       3 2 4 4       3 3 3 3       3 4 2 2
b d x  + 6 b c d x  + 15 b c d x  + 20 b c d x  + 15 b c d x
+
3 5       3 6
6 b c d x + b c
*
3       2 2                  2          a log(F)
log(F) Ei((b d x  + 2 b c d x + b c )log(F))%e
/
7 6         6 5        2 5 4        3 4 3        4 3 2       5 2
12 d x  + 72 c d x  + 180 c d x  + 240 c d x  + 180 c d x  + 72 c d x
+
6
12 c d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^9, x)
(70)
3 6 6      3   5 5       3 2 4 4       3 3 3 3       3 4 2 2
- b d x  - 6 b c d x  - 15 b c d x  - 20 b c d x  - 15 b c d x
+
3 5       3 6
- 6 b c d x - b c
*
3
log(F)
+
2 4 4      2   3 3      2 2 2 2      2 3       2 4       2
(- b d x  - 4 b c d x  - 6 b c d x  - 4 b c d x - b c )log(F)
+
2 2                    2
(- 2 b d x  - 4 b c d x - 2 b c )log(F) - 6
*
2 2                  2
(b d x  + 2 b c d x + b c  + a)log(F)
%e
+
4 8 8      4   7 7       4 2 6 6       4 3 5 5       4 4 4 4
b d x  + 8 b c d x  + 28 b c d x  + 56 b c d x  + 70 b c d x
+
4 5 3 3       4 6 2 2      4 7       4 8
56 b c d x  + 28 b c d x  + 8 b c d x + b c
*
4       2 2                  2          a log(F)
log(F) Ei((b d x  + 2 b c d x + b c )log(F))%e
/
9 8          8 7         2 7 6         3 6 5         4 5 4
48 d x  + 384 c d x  + 1344 c d x  + 2688 c d x  + 3360 c d x
+
5 4 3         6 3 2        7 2        8
2688 c d x  + 1344 c d x  + 384 c d x + 48 c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^11, x)
(71)
4 8 8      4   7 7       4 2 6 6       4 3 5 5       4 4 4 4
- b d x  - 8 b c d x  - 28 b c d x  - 56 b c d x  - 70 b c d x
+
4 5 3 3       4 6 2 2      4 7       4 8
- 56 b c d x  - 28 b c d x  - 8 b c d x - b c
*
4
log(F)
+
3 6 6      3   5 5       3 2 4 4       3 3 3 3       3 4 2 2
- b d x  - 6 b c d x  - 15 b c d x  - 20 b c d x  - 15 b c d x
+
3 5       3 6
- 6 b c d x - b c
*
3
log(F)
+
2 4 4      2   3 3       2 2 2 2      2 3         2 4       2
(- 2 b d x  - 8 b c d x  - 12 b c d x  - 8 b c d x - 2 b c )log(F)
+
2 2                     2
(- 6 b d x  - 12 b c d x - 6 b c )log(F) - 24
*
2 2                  2
(b d x  + 2 b c d x + b c  + a)log(F)
%e
+
5 10 10       5   9 9       5 2 8 8        5 3 7 7        5 4 6 6
b d  x   + 10 b c d x  + 45 b c d x  + 120 b c d x  + 210 b c d x
+
5 5 5 5        5 6 4 4        5 7 3 3       5 8 2 2       5 9
252 b c d x  + 210 b c d x  + 120 b c d x  + 45 b c d x  + 10 b c d x
+
5 10
b c
*
5       2 2                  2          a log(F)
log(F) Ei((b d x  + 2 b c d x + b c )log(F))%e
/
11 10           10 9          2 9 8          3 8 7          4 7 6
240 d  x   + 2400 c d  x  + 10800 c d x  + 28800 c d x  + 50400 c d x
+
5 6 5          6 5 4          7 4 3          8 3 2         9 2
60480 c d x  + 50400 c d x  + 28800 c d x  + 10800 c d x  + 2400 c d x
+
10
240 c  d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^12, x)
(72)
+------------+
|     2
+---+  a log(F)    (d x + c)\|- b d log(F)
10395 d\|%pi %e        erf(------------------------)
d
+
5 11 11        5   10 10         5 2 9 9          5 3 8 8
64 b d  x   + 704 b c d  x   + 3520 b c d x  + 10560 b c d x
+
5 4 7 7          5 5 6 6          5 6 5 5          5 7 4 4
21120 b c d x  + 29568 b c d x  + 29568 b c d x  + 21120 b c d x
+
5 8 3 3         5 9 2 2        5 10          5 11
10560 b c d x  + 3520 b c d x  + 704 b c  d x + 64 b c
*
5
log(F)
+
4 9 9         4   8 8          4 2 7 7          4 3 6 6
- 352 b d x  - 3168 b c d x  - 12672 b c d x  - 29568 b c d x
+
4 4 5 5          4 5 4 4          4 6 3 3
- 44352 b c d x  - 44352 b c d x  - 29568 b c d x
+
4 7 2 2         4 8           4 9
- 12672 b c d x  - 3168 b c d x - 352 b c
*
4
log(F)
+
3 7 7          3   6 6          3 2 5 5          3 3 4 4
1584 b d x  + 11088 b c d x  + 33264 b c d x  + 55440 b c d x
+
3 4 3 3          3 5 2 2          3 6            3 7
55440 b c d x  + 33264 b c d x  + 11088 b c d x + 1584 b c
*
3
log(F)
+
2 5 5          2   4 4          2 2 3 3          2 3 2 2
- 5544 b d x  - 27720 b c d x  - 55440 b c d x  - 55440 b c d x
+
2 4            2 5
- 27720 b c d x - 5544 b c
*
2
log(F)
+
3 3              2 2            2               3
(13860 b d x  + 41580 b c d x  + 41580 b c d x + 13860 b c )log(F)
+
- 20790 d x - 20790 c
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
+------------+
6        6 |     2
128 b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^10, x)
(73)
+------------+
|     2
+---+  a log(F)    (d x + c)\|- b d log(F)
- 945 d\|%pi %e        erf(------------------------)
d
+
4 9 9        4   8 8         4 2 7 7         4 3 6 6
32 b d x  + 288 b c d x  + 1152 b c d x  + 2688 b c d x
+
4 4 5 5         4 5 4 4         4 6 3 3         4 7 2 2
4032 b c d x  + 4032 b c d x  + 2688 b c d x  + 1152 b c d x
+
4 8          4 9
288 b c d x + 32 b c
*
4
log(F)
+
3 7 7         3   6 6         3 2 5 5         3 3 4 4
- 144 b d x  - 1008 b c d x  - 3024 b c d x  - 5040 b c d x
+
3 4 3 3         3 5 2 2         3 6           3 7
- 5040 b c d x  - 3024 b c d x  - 1008 b c d x - 144 b c
*
3
log(F)
+
2 5 5         2   4 4         2 2 3 3         2 3 2 2
504 b d x  + 2520 b c d x  + 5040 b c d x  + 5040 b c d x
+
2 4           2 5
2520 b c d x + 504 b c
*
2
log(F)
+
3 3             2 2           2              3
(- 1260 b d x  - 3780 b c d x  - 3780 b c d x - 1260 b c )log(F)
+
1890 d x + 1890 c
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
+------------+
5        5 |     2
64 b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^8, x)
(74)
+------------+
|     2
+---+  a log(F)    (d x + c)\|- b d log(F)
105 d\|%pi %e        erf(------------------------)
d
+
3 7 7        3   6 6        3 2 5 5        3 3 4 4
16 b d x  + 112 b c d x  + 336 b c d x  + 560 b c d x
+
3 4 3 3        3 5 2 2        3 6          3 7
560 b c d x  + 336 b c d x  + 112 b c d x + 16 b c
*
3
log(F)
+
2 5 5        2   4 4        2 2 3 3        2 3 2 2
- 56 b d x  - 280 b c d x  - 560 b c d x  - 560 b c d x
+
2 4          2 5
- 280 b c d x - 56 b c
*
2
log(F)
+
3 3            2 2          2             3
(140 b d x  + 420 b c d x  + 420 b c d x + 140 b c )log(F) - 210 d x
+
- 210 c
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
+------------+
4        4 |     2
32 b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^6, x)
(75)
+------------+
|     2
+---+  a log(F)    (d x + c)\|- b d log(F)
- 15 d\|%pi %e        erf(------------------------)
d
+
2 5 5       2   4 4       2 2 3 3       2 3 2 2       2 4
8 b d x  + 40 b c d x  + 80 b c d x  + 80 b c d x  + 40 b c d x
+
2 5
8 b c
*
2
log(F)
+
3 3           2 2         2            3
(- 20 b d x  - 60 b c d x  - 60 b c d x - 20 b c )log(F) + 30 d x
+
30 c
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
+------------+
3        3 |     2
16 b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^4, x)
(76)
+------------+
|     2
+---+  a log(F)    (d x + c)\|- b d log(F)
3 d\|%pi %e        erf(------------------------)
d
+
3 3           2 2         2           3
((4 b d x  + 12 b c d x  + 12 b c d x + 4 b c )log(F) - 6 d x - 6 c)
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
+------------+
2        2 |     2
8 b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^2, x)
(77)
+------------+
|     2
+---+  a log(F)    (d x + c)\|- b d log(F)
- d\|%pi %e        erf(------------------------)
d
+
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
(2 d x + 2 c)%e                                     \|- b d log(F)
/
+------------+
|     2
4 b d log(F)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2), x)
+------------+
|     2
+---+  a log(F)    (d x + c)\|- b d log(F)
\|%pi %e        erf(------------------------)
d
(78)  ---------------------------------------------
+------------+
|     2
2 \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^2, x)
(79)
+------------+
|     2
2                 +---+  a log(F)    (d x + c)\|- b d log(F)
(b d x + b c d)log(F)\|%pi %e        erf(------------------------)
d
+
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
- %e                                     \|- b d log(F)
/
+------------+
2         |     2
(d x + c d)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^4, x)
(80)
2 4 3      2   3 2      2 2 2       2 3        2 +---+  a log(F)
(2 b d x  + 6 b c d x  + 6 b c d x + 2 b c d)log(F) \|%pi %e
*
+------------+
|     2
(d x + c)\|- b d log(F)
erf(------------------------)
d
+
2 2                    2
((- 2 b d x  - 4 b c d x - 2 b c )log(F) - 1)
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
+------------+
4 3        3 2      2 2       3   |     2
(3 d x  + 9 c d x  + 9 c d x + 3 c d)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^6, x)
(81)
3 6 5       3   5 4       3 2 4 3       3 3 3 2       3 4 2
4 b d x  + 20 b c d x  + 40 b c d x  + 40 b c d x  + 20 b c d x
+
3 5
4 b c d
*
+------------+
|     2
3 +---+  a log(F)    (d x + c)\|- b d log(F)
log(F) \|%pi %e        erf(------------------------)
d
+
2 4 4       2   3 3       2 2 2 2       2 3         2 4       2
(- 4 b d x  - 16 b c d x  - 24 b c d x  - 16 b c d x - 4 b c )log(F)
+
2 2                    2
(- 2 b d x  - 4 b c d x - 2 b c )log(F) - 3
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
6 5         5 4        2 4 3        3 3 2       4 2        5
(15 d x  + 75 c d x  + 150 c d x  + 150 c d x  + 75 c d x + 15 c d)
*
+------------+
|     2
\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^8, x)
(82)
4 8 7       4   7 6        4 2 6 5        4 3 5 4        4 4 4 3
8 b d x  + 56 b c d x  + 168 b c d x  + 280 b c d x  + 280 b c d x
+
4 5 3 2       4 6 2       4 7
168 b c d x  + 56 b c d x + 8 b c d
*
+------------+
|     2
4 +---+  a log(F)    (d x + c)\|- b d log(F)
log(F) \|%pi %e        erf(------------------------)
d
+
3 6 6       3   5 5        3 2 4 4        3 3 3 3
- 8 b d x  - 48 b c d x  - 120 b c d x  - 160 b c d x
+
3 4 2 2       3 5         3 6
- 120 b c d x  - 48 b c d x - 8 b c
*
3
log(F)
+
2 4 4       2   3 3       2 2 2 2       2 3         2 4       2
(- 4 b d x  - 16 b c d x  - 24 b c d x  - 16 b c d x - 4 b c )log(F)
+
2 2                     2
(- 6 b d x  - 12 b c d x - 6 b c )log(F) - 15
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
8 7          7 6         2 6 5         3 5 4         4 4 3
105 d x  + 735 c d x  + 2205 c d x  + 3675 c d x  + 3675 c d x
+
5 3 2        6 2         7
2205 c d x  + 735 c d x + 105 c d
*
+------------+
|     2
\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^10, x)
(83)
5 10 9        5   9 8        5 2 8 7         5 3 7 6
16 b d  x  + 144 b c d x  + 576 b c d x  + 1344 b c d x
+
5 4 6 5         5 5 5 4         5 6 4 3        5 7 3 2
2016 b c d x  + 2016 b c d x  + 1344 b c d x  + 576 b c d x
+
5 8 2        5 9
144 b c d x + 16 b c d
*
+------------+
|     2
5 +---+  a log(F)    (d x + c)\|- b d log(F)
log(F) \|%pi %e        erf(------------------------)
d
+
4 8 8        4   7 7        4 2 6 6        4 3 5 5
- 16 b d x  - 128 b c d x  - 448 b c d x  - 896 b c d x
+
4 4 4 4        4 5 3 3        4 6 2 2        4 7
- 1120 b c d x  - 896 b c d x  - 448 b c d x  - 128 b c d x
+
4 8
- 16 b c
*
4
log(F)
+
3 6 6       3   5 5        3 2 4 4        3 3 3 3
- 8 b d x  - 48 b c d x  - 120 b c d x  - 160 b c d x
+
3 4 2 2       3 5         3 6
- 120 b c d x  - 48 b c d x - 8 b c
*
3
log(F)
+
2 4 4       2   3 3       2 2 2 2       2 3          2 4
(- 12 b d x  - 48 b c d x  - 72 b c d x  - 48 b c d x - 12 b c )
*
2
log(F)
+
2 2                      2
(- 30 b d x  - 60 b c d x - 30 b c )log(F) - 105
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
10 9           9 8          2 8 7          3 7 6           4 6 5
945 d  x  + 8505 c d x  + 34020 c d x  + 79380 c d x  + 119070 c d x
+
5 5 4          6 4 3          7 3 2         8 2         9
119070 c d x  + 79380 c d x  + 34020 c d x  + 8505 c d x + 945 c d
*
+------------+
|     2
\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^12, x)
(84)
6 12 11        6   11 10         6 2 10 9         6 3 9 8
32 b d  x   + 352 b c d  x   + 1760 b c d  x  + 5280 b c d x
+
6 4 8 7          6 5 7 6          6 6 6 5          6 7 5 4
10560 b c d x  + 14784 b c d x  + 14784 b c d x  + 10560 b c d x
+
6 8 4 3         6 9 3 2        6 10 2        6 11
5280 b c d x  + 1760 b c d x  + 352 b c  d x + 32 b c  d
*
+------------+
|     2
6 +---+  a log(F)    (d x + c)\|- b d log(F)
log(F) \|%pi %e        erf(------------------------)
d
+
5 10 10        5   9 9         5 2 8 8         5 3 7 7
- 32 b d  x   - 320 b c d x  - 1440 b c d x  - 3840 b c d x
+
5 4 6 6         5 5 5 5         5 6 4 4         5 7 3 3
- 6720 b c d x  - 8064 b c d x  - 6720 b c d x  - 3840 b c d x
+
5 8 2 2        5 9          5 10
- 1440 b c d x  - 320 b c d x - 32 b c
*
5
log(F)
+
4 8 8        4   7 7        4 2 6 6        4 3 5 5
- 16 b d x  - 128 b c d x  - 448 b c d x  - 896 b c d x
+
4 4 4 4        4 5 3 3        4 6 2 2        4 7
- 1120 b c d x  - 896 b c d x  - 448 b c d x  - 128 b c d x
+
4 8
- 16 b c
*
4
log(F)
+
3 6 6        3   5 5        3 2 4 4        3 3 3 3
- 24 b d x  - 144 b c d x  - 360 b c d x  - 480 b c d x
+
3 4 2 2        3 5          3 6
- 360 b c d x  - 144 b c d x - 24 b c
*
3
log(F)
+
2 4 4        2   3 3        2 2 2 2        2 3          2 4
(- 60 b d x  - 240 b c d x  - 360 b c d x  - 240 b c d x - 60 b c )
*
2
log(F)
+
2 2                        2
(- 210 b d x  - 420 b c d x - 210 b c )log(F) - 945
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
12 11             11 10           2 10 9            3 9 8
10395 d  x   + 114345 c d  x   + 571725 c d  x  + 1715175 c d x
+
4 8 7            5 7 6            6 6 5            7 5 4
3430350 c d x  + 4802490 c d x  + 4802490 c d x  + 3430350 c d x
+
8 4 3           9 3 2           10 2           11
1715175 c d x  + 571725 c d x  + 114345 c  d x + 10395 c  d
*
+------------+
|     2
\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^m, x)
(85)
m + 1       3 3          2 2        2         3
Gamma(-----,(- b d x  - 3 b c d x  - 3 b c d x - b c )log(F))
3
*
(- m + 2)log(- b log(F)) + 3 a log(F)
-------------------------------------
3
%e
/
3 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^17, x)
(86)
5 15 15       5   14 14        5 2 13 13        5 3 12 12
b d  x   + 15 b c d  x   + 105 b c d  x   + 455 b c d  x
+
5 4 11 11         5 5 10 10         5 6 9 9         5 7 8 8
1365 b c d  x   + 3003 b c d  x   + 5005 b c d x  + 6435 b c d x
+
5 8 7 7         5 9 6 6         5 10 5 5         5 11 4 4
6435 b c d x  + 5005 b c d x  + 3003 b c  d x  + 1365 b c  d x
+
5 12 3 3        5 13 2 2       5 14       5 15
455 b c  d x  + 105 b c  d x  + 15 b c  d x + b c
*
5
log(F)
+
4 12 12       4   11 11        4 2 10 10         4 3 9 9
- 5 b d  x   - 60 b c d  x   - 330 b c d  x   - 1100 b c d x
+
4 4 8 8         4 5 7 7         4 6 6 6         4 7 5 5
- 2475 b c d x  - 3960 b c d x  - 4620 b c d x  - 3960 b c d x
+
4 8 4 4         4 9 3 3        4 10 2 2       4 11
- 2475 b c d x  - 1100 b c d x  - 330 b c  d x  - 60 b c  d x
+
4 12
- 5 b c
*
4
log(F)
+
3 9 9        3   8 8        3 2 7 7         3 3 6 6
20 b d x  + 180 b c d x  + 720 b c d x  + 1680 b c d x
+
3 4 5 5         3 5 4 4         3 6 3 3        3 7 2 2
2520 b c d x  + 2520 b c d x  + 1680 b c d x  + 720 b c d x
+
3 8          3 9
180 b c d x + 20 b c
*
3
log(F)
+
2 6 6        2   5 5        2 2 4 4         2 3 3 3
- 60 b d x  - 360 b c d x  - 900 b c d x  - 1200 b c d x
+
2 4 2 2        2 5          2 6
- 900 b c d x  - 360 b c d x - 60 b c
*
2
log(F)
+
3 3            2 2          2             3
(120 b d x  + 360 b c d x  + 360 b c d x + 120 b c )log(F) - 120
*
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
%e
/
6        6
3 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^14, x)
(87)
4 12 12       4   11 11       4 2 10 10        4 3 9 9
b d  x   + 12 b c d  x   + 66 b c d  x   + 220 b c d x
+
4 4 8 8        4 5 7 7        4 6 6 6        4 7 5 5
495 b c d x  + 792 b c d x  + 924 b c d x  + 792 b c d x
+
4 8 4 4        4 9 3 3       4 10 2 2       4 11       4 12
495 b c d x  + 220 b c d x  + 66 b c  d x  + 12 b c  d x + b c
*
4
log(F)
+
3 9 9       3   8 8        3 2 7 7        3 3 6 6
- 4 b d x  - 36 b c d x  - 144 b c d x  - 336 b c d x
+
3 4 5 5        3 5 4 4        3 6 3 3        3 7 2 2
- 504 b c d x  - 504 b c d x  - 336 b c d x  - 144 b c d x
+
3 8         3 9
- 36 b c d x - 4 b c
*
3
log(F)
+
2 6 6       2   5 5        2 2 4 4        2 3 3 3
12 b d x  + 72 b c d x  + 180 b c d x  + 240 b c d x
+
2 4 2 2       2 5          2 6
180 b c d x  + 72 b c d x + 12 b c
*
2
log(F)
+
3 3           2 2         2            3
(- 24 b d x  - 72 b c d x  - 72 b c d x - 24 b c )log(F) + 24
*
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
%e
/
5        5
3 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^11, x)
(88)
3 9 9      3   8 8       3 2 7 7       3 3 6 6        3 4 5 5
b d x  + 9 b c d x  + 36 b c d x  + 84 b c d x  + 126 b c d x
+
3 5 4 4       3 6 3 3       3 7 2 2      3 8       3 9
126 b c d x  + 84 b c d x  + 36 b c d x  + 9 b c d x + b c
*
3
log(F)
+
2 6 6       2   5 5       2 2 4 4       2 3 3 3       2 4 2 2
- 3 b d x  - 18 b c d x  - 45 b c d x  - 60 b c d x  - 45 b c d x
+
2 5         2 6
- 18 b c d x - 3 b c
*
2
log(F)
+
3 3           2 2         2           3
(6 b d x  + 18 b c d x  + 18 b c d x + 6 b c )log(F) - 6
*
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
%e
/
4        4
3 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^8, x)
(89)
2 6 6      2   5 5       2 2 4 4       2 3 3 3       2 4 2 2
b d x  + 6 b c d x  + 15 b c d x  + 20 b c d x  + 15 b c d x
+
2 5       2 6
6 b c d x + b c
*
2
log(F)
+
3 3          2 2        2           3
(- 2 b d x  - 6 b c d x  - 6 b c d x - 2 b c )log(F) + 2
*
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
%e
/
3        3
3 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^5, x)
(90)
3 3          2 2        2         3
((b d x  + 3 b c d x  + 3 b c d x + b c )log(F) - 1)
*
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
%e
/
2        2
3 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^2, x)
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
%e
(91)  ----------------------------------------------------
3 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x), x)
3 3          2 2        2         3          a log(F)
Ei((b d x  + 3 b c d x  + 3 b c d x + b c )log(F))%e
(92)  ------------------------------------------------------------
3 d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^4, x)
(93)
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
- %e
+
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c )log(F)
*
3 3          2 2        2         3          a log(F)
Ei((b d x  + 3 b c d x  + 3 b c d x + b c )log(F))%e
/
4 3        3 2      2 2       3
3 d x  + 9 c d x  + 9 c d x + 3 c d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^7, x)
(94)
3 3          2 2        2         3
((- b d x  - 3 b c d x  - 3 b c d x - b c )log(F) - 1)
*
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
%e
+
2 6 6      2   5 5       2 2 4 4       2 3 3 3       2 4 2 2
b d x  + 6 b c d x  + 15 b c d x  + 20 b c d x  + 15 b c d x
+
2 5       2 6
6 b c d x + b c
*
2       3 3          2 2        2         3          a log(F)
log(F) Ei((b d x  + 3 b c d x  + 3 b c d x + b c )log(F))%e
/
7 6         6 5       2 5 4        3 4 3       4 3 2       5 2       6
6 d x  + 36 c d x  + 90 c d x  + 120 c d x  + 90 c d x  + 36 c d x + 6 c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^10, x)
(95)
2 6 6      2   5 5       2 2 4 4       2 3 3 3       2 4 2 2
- b d x  - 6 b c d x  - 15 b c d x  - 20 b c d x  - 15 b c d x
+
2 5       2 6
- 6 b c d x - b c
*
2
log(F)
+
3 3          2 2        2         3
(- b d x  - 3 b c d x  - 3 b c d x - b c )log(F) - 2
*
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
%e
+
3 9 9      3   8 8       3 2 7 7       3 3 6 6        3 4 5 5
b d x  + 9 b c d x  + 36 b c d x  + 84 b c d x  + 126 b c d x
+
3 5 4 4       3 6 3 3       3 7 2 2      3 8       3 9
126 b c d x  + 84 b c d x  + 36 b c d x  + 9 b c d x + b c
*
3       3 3          2 2        2         3          a log(F)
log(F) Ei((b d x  + 3 b c d x  + 3 b c d x + b c )log(F))%e
/
10 9          9 8        2 8 7         3 7 6         4 6 5
18 d  x  + 162 c d x  + 648 c d x  + 1512 c d x  + 2268 c d x
+
5 5 4         6 4 3        7 3 2        8 2        9
2268 c d x  + 1512 c d x  + 648 c d x  + 162 c d x + 18 c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^13, x)
(96)
3 9 9      3   8 8       3 2 7 7       3 3 6 6        3 4 5 5
- b d x  - 9 b c d x  - 36 b c d x  - 84 b c d x  - 126 b c d x
+
3 5 4 4       3 6 3 3       3 7 2 2      3 8       3 9
- 126 b c d x  - 84 b c d x  - 36 b c d x  - 9 b c d x - b c
*
3
log(F)
+
2 6 6      2   5 5       2 2 4 4       2 3 3 3       2 4 2 2
- b d x  - 6 b c d x  - 15 b c d x  - 20 b c d x  - 15 b c d x
+
2 5       2 6
- 6 b c d x - b c
*
2
log(F)
+
3 3          2 2        2           3
(- 2 b d x  - 6 b c d x  - 6 b c d x - 2 b c )log(F) - 6
*
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
%e
+
4 12 12       4   11 11       4 2 10 10        4 3 9 9
b d  x   + 12 b c d  x   + 66 b c d  x   + 220 b c d x
+
4 4 8 8        4 5 7 7        4 6 6 6        4 7 5 5
495 b c d x  + 792 b c d x  + 924 b c d x  + 792 b c d x
+
4 8 4 4        4 9 3 3       4 10 2 2       4 11       4 12
495 b c d x  + 220 b c d x  + 66 b c  d x  + 12 b c  d x + b c
*
4       3 3          2 2        2         3          a log(F)
log(F) Ei((b d x  + 3 b c d x  + 3 b c d x + b c )log(F))%e
/
13 12          12 11         2 11 10          3 10 9          4 9 8
72 d  x   + 864 c d  x   + 4752 c d  x   + 15840 c d  x  + 35640 c d x
+
5 8 7          6 7 6          7 6 5          8 5 4          9 4 3
57024 c d x  + 66528 c d x  + 57024 c d x  + 35640 c d x  + 15840 c d x
+
10 3 2        11 2        12
4752 c  d x  + 864 c  d x + 72 c  d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^16, x)
(97)
4 12 12       4   11 11       4 2 10 10        4 3 9 9
- b d  x   - 12 b c d  x   - 66 b c d  x   - 220 b c d x
+
4 4 8 8        4 5 7 7        4 6 6 6        4 7 5 5
- 495 b c d x  - 792 b c d x  - 924 b c d x  - 792 b c d x
+
4 8 4 4        4 9 3 3       4 10 2 2       4 11       4 12
- 495 b c d x  - 220 b c d x  - 66 b c  d x  - 12 b c  d x - b c
*
4
log(F)
+
3 9 9      3   8 8       3 2 7 7       3 3 6 6        3 4 5 5
- b d x  - 9 b c d x  - 36 b c d x  - 84 b c d x  - 126 b c d x
+
3 5 4 4       3 6 3 3       3 7 2 2      3 8       3 9
- 126 b c d x  - 84 b c d x  - 36 b c d x  - 9 b c d x - b c
*
3
log(F)
+
2 6 6       2   5 5       2 2 4 4       2 3 3 3
- 2 b d x  - 12 b c d x  - 30 b c d x  - 40 b c d x
+
2 4 2 2       2 5         2 6
- 30 b c d x  - 12 b c d x - 2 b c
*
2
log(F)
+
3 3           2 2         2           3
(- 6 b d x  - 18 b c d x  - 18 b c d x - 6 b c )log(F) - 24
*
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
%e
+
5 15 15       5   14 14        5 2 13 13        5 3 12 12
b d  x   + 15 b c d  x   + 105 b c d  x   + 455 b c d  x
+
5 4 11 11         5 5 10 10         5 6 9 9         5 7 8 8
1365 b c d  x   + 3003 b c d  x   + 5005 b c d x  + 6435 b c d x
+
5 8 7 7         5 9 6 6         5 10 5 5         5 11 4 4
6435 b c d x  + 5005 b c d x  + 3003 b c  d x  + 1365 b c  d x
+
5 12 3 3        5 13 2 2       5 14       5 15
455 b c  d x  + 105 b c  d x  + 15 b c  d x + b c
*
5       3 3          2 2        2         3          a log(F)
log(F) Ei((b d x  + 3 b c d x  + 3 b c d x + b c )log(F))%e
/
16 15           15 14          2 14 13           3 13 12
360 d  x   + 5400 c d  x   + 37800 c d  x   + 163800 c d  x
+
4 12 11            5 11 10            6 10 9            7 9 8
491400 c d  x   + 1081080 c d  x   + 1801800 c d  x  + 2316600 c d x
+
8 8 7            9 7 6            10 6 5           11 5 4
2316600 c d x  + 1801800 c d x  + 1081080 c  d x  + 491400 c  d x
+
12 4 3          13 3 2         14 2         15
163800 c  d x  + 37800 c  d x  + 5400 c  d x + 360 c  d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^3, x)
(98)
3 3          2 2        2         3
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F)
(3 d x + 3 c)%e
*
+------------+
3|     3
\|- b d log(F)
+
a log(F)      1       3 3          2 2        2         3
d %e        Gamma(-,(- b d x  - 3 b c d x  - 3 b c d x - b c )log(F))
3
/
+------------+
3|     3
9 b d log(F)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x), x)
(99)
a log(F)      2       3 3          2 2        2         3
d %e        Gamma(-,(- b d x  - 3 b c d x  - 3 b c d x - b c )log(F))
3
- ---------------------------------------------------------------------
+------------+2
3|     3
3 \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^3), x)
(100)
a log(F)      1       3 3          2 2        2         3
%e        Gamma(-,(- b d x  - 3 b c d x  - 3 b c d x - b c )log(F))
3
- -------------------------------------------------------------------
+------------+
3|     3
3 \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^2, x)
(101)
3 3          2 2        2         3             +------------+2
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F) 3|     3
- %e                                                   \|- b d log(F)
+
3         2         a log(F)
(- b d x - b c d )log(F)%e
*
2       3 3          2 2        2         3
Gamma(-,(- b d x  - 3 b c d x  - 3 b c d x - b c )log(F))
3
/
+------------+2
2        3|     3
(d x + c d)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^3, x)
(102)
3 3          2 2        2         3             +------------+
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F) 3|     3
- %e                                                   \|- b d log(F)
+
3 2          2       2          a log(F)
(- b d x  - 2 b c d x - b c d)log(F)%e
*
1       3 3          2 2        2         3
Gamma(-,(- b d x  - 3 b c d x  - 3 b c d x - b c )log(F))
3
/
+------------+
3 2        2       2  3|     3
(2 d x  + 4 c d x + 2 c d)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^5, x)
(103)
3 3          2 2        2           3
((- 3 b d x  - 9 b c d x  - 9 b c d x - 3 b c )log(F) - 1)
*
3 3          2 2        2         3             +------------+2
(b d x  + 3 b c d x  + 3 b c d x + b c  + a)log(F) 3|     3
%e                                                   \|- b d log(F)
+
2 6 4       2   5 3       2 2 4 2       2 3 3       2 4 2       2
(- 3 b d x  - 12 b c d x  - 18 b c d x  - 12 b c d x - 3 b c d )log(F)
*
a log(F)      2       3 3          2 2        2         3
%e        Gamma(-,(- b d x  - 3 b c d x  - 3 b c d x - b c )log(F))
3
/
+------------+2
5 4         4 3       2 3 2       3 2       4  3|     3
(4 d x  + 16 c d x  + 24 c d x  + 16 c d x + 4 c d)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*(c+d*x)^(1/2)), x)
+-------+
+-------+       b log(f)\|d x + c  + a log(f)
(2 b log(f)\|d x + c  - 2)%e
(104)  ---------------------------------------------------------
2        2
b d log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*(c+d*x)^(1/3)), x)
(105)
2      2 3+-------+2             3+-------+
(3 b log(f)  \|d x + c   - 6 b log(f)\|d x + c  + 6)
*
3+-------+
b log(f)\|d x + c  + a log(f)
%e
/
3        3
b d log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- n<0
integrate(F^(a+b/(c+d*x))*(c+d*x)^m, x)
%A a d + a c + b
x  ----------------
++       %A d + c              m
(106)   |   F                (%A d + c) d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.01 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x))*(c+d*x)^4, x)
(107)
4       4        4     3 2 2      3         3 2       3
(b d x + b c)log(F)  + (b d x  + 2 b c d x + b c )log(F)
+
2 3 3      2   2 2      2 2         2 3       2
(2 b d x  + 6 b c d x  + 6 b c d x + 2 b c )log(F)
+
4 4           3 3         2 2 2         3           4
(6 b d x  + 24 b c d x  + 36 b c d x  + 24 b c d x + 6 b c )log(F)
+
5 5          4 4        2 3 3        3 2 2        4          5
24 d x  + 120 c d x  + 240 c d x  + 240 c d x  + 120 c d x + 24 c
*
(a d x + a c + b)log(F)
-----------------------
d x + c
%e
+
5      5   b log(F)   a log(F)
- b log(F) Ei(--------)%e
d x + c
/
120 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))*(c+d*x)^3, x)
(108)
3       3        3     2 2 2      2         2 2       2
(b d x + b c)log(F)  + (b d x  + 2 b c d x + b c )log(F)
+
3 3          2 2        2           3             4 4
(2 b d x  + 6 b c d x  + 6 b c d x + 2 b c )log(F) + 6 d x
+
3 3       2 2 2       3         4
24 c d x  + 36 c d x  + 24 c d x + 6 c
*
(a d x + a c + b)log(F)
-----------------------
d x + c
%e
+
4      4   b log(F)   a log(F)
- b log(F) Ei(--------)%e
d x + c
/
24 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))*(c+d*x)^2, x)
(109)
2       2        2       2 2                  2             3 3
(b d x + b c)log(F)  + (b d x  + 2 b c d x + b c )log(F) + 2 d x
+
2 2      2         3
6 c d x  + 6 c d x + 2 c
*
(a d x + a c + b)log(F)
-----------------------
d x + c
%e
+
3      3   b log(F)   a log(F)
- b log(F) Ei(--------)%e
d x + c
/
6 d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x))*(c+d*x), x)
(110)
(a d x + a c + b)log(F)
-----------------------
2 2              2           d x + c
((b d x + b c)log(F) + d x  + 2 c d x + c )%e
+
2      2   b log(F)   a log(F)
- b log(F) Ei(--------)%e
d x + c
/
2 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)), x)
(a d x + a c + b)log(F)
-----------------------
d x + c                      b log(F)   a log(F)
(d x + c)%e                        - b log(F)Ei(--------)%e
d x + c
(111)  -------------------------------------------------------------------
d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x))/(c+d*x), x)
b log(F)   a log(F)
Ei(--------)%e
d x + c
(112)  - ----------------------
d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^2, x)
(a d x + a c + b)log(F)
-----------------------
d x + c
%e
(113)  - -------------------------
b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^3, x)
(a d x + a c + b)log(F)
-----------------------
d x + c
(- b log(F) + d x + c)%e
(114)  -----------------------------------------------
2 2     2          2
(b d x + b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^4, x)
(115)
2      2                                2 2                2
(- b log(F)  + (2 b d x + 2 b c)log(F) - 2 d x  - 4 c d x - 2 c )
*
(a d x + a c + b)log(F)
-----------------------
d x + c
%e
/
3 3 2      3   2     3 2        3
(b d x  + 2 b c d x + b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^5, x)
(116)
3      3       2         2        2
- b log(F)  + (3 b d x + 3 b c)log(F)
+
2 2                     2             3 3         2 2
(- 6 b d x  - 12 b c d x - 6 b c )log(F) + 6 d x  + 18 c d x
+
2         3
18 c d x + 6 c
*
(a d x + a c + b)log(F)
-----------------------
d x + c
%e
/
4 4 3      4   3 2      4 2 2     4 3        4
(b d x  + 3 b c d x  + 3 b c d x + b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^6, x)
(117)
4      4       3         3        3
- b log(F)  + (4 b d x + 4 b c)log(F)
+
2 2 2       2            2 2       2
(- 12 b d x  - 24 b c d x - 12 b c )log(F)
+
3 3           2 2         2            3              4 4
(24 b d x  + 72 b c d x  + 72 b c d x + 24 b c )log(F) - 24 d x
+
3 3        2 2 2       3          4
- 96 c d x  - 144 c d x  - 96 c d x - 24 c
*
(a d x + a c + b)log(F)
-----------------------
d x + c
%e
/
5 5 4      5   4 3      5 2 3 2      5 3 2     5 4        5
(b d x  + 4 b c d x  + 6 b c d x  + 4 b c d x + b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.01 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^7, x)
(118)
5      5       4         4        4
- b log(F)  + (5 b d x + 5 b c)log(F)
+
3 2 2       3            3 2       3
(- 20 b d x  - 40 b c d x - 20 b c )log(F)
+
2 3 3        2   2 2        2 2          2 3       2
(60 b d x  + 180 b c d x  + 180 b c d x + 60 b c )log(F)
+
4 4            3 3          2 2 2          3             4
(- 120 b d x  - 480 b c d x  - 720 b c d x  - 480 b c d x - 120 b c )
*
log(F)
+
5 5          4 4         2 3 3         3 2 2        4           5
120 d x  + 600 c d x  + 1200 c d x  + 1200 c d x  + 600 c d x + 120 c
*
(a d x + a c + b)log(F)
-----------------------
d x + c
%e
/
6 6 5      6   5 4       6 2 4 3       6 3 3 2      6 4 2     6 5
(b d x  + 5 b c d x  + 10 b c d x  + 10 b c d x  + 5 b c d x + b c d)
*
6
log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^m, x)
2   2                   2
%A a d  + 2 %A a c d + a c  + b
-------------------------------
x         2 2               2
++        %A d  + 2 %A c d + c                m
(119)   |   F                               (%A d + c) d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^9, x)
(120)
4 2 2      4         4 2       4
(b d x  + 2 b c d x + b c )log(F)
+
3 4 4      3   3 3      3 2 2 2      3 3       3 4       3
(b d x  + 4 b c d x  + 6 b c d x  + 4 b c d x + b c )log(F)
+
2 6 6       2   5 5       2 2 4 4       2 3 3 3       2 4 2 2
2 b d x  + 12 b c d x  + 30 b c d x  + 40 b c d x  + 30 b c d x
+
2 5         2 6
12 b c d x + 2 b c
*
2
log(F)
+
8 8           7 7          2 6 6          3 5 5
6 b d x  + 48 b c d x  + 168 b c d x  + 336 b c d x
+
4 4 4          5 3 3          6 2 2         7           8
420 b c d x  + 336 b c d x  + 168 b c d x  + 48 b c d x + 6 b c
*
log(F)
+
10 10          9 9         2 8 8         3 7 7         4 6 6
24 d  x   + 240 c d x  + 1080 c d x  + 2880 c d x  + 5040 c d x
+
5 5 5         6 4 4         7 3 3         8 2 2        9
6048 c d x  + 5040 c d x  + 2880 c d x  + 1080 c d x  + 240 c d x
+
10
24 c
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2
d x  + 2 c d x + c
%e
+
5      5         b log(F)        a log(F)
- b log(F) Ei(-------------------)%e
2 2              2
d x  + 2 c d x + c
/
240 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^7, x)
(121)
3 2 2      3         3 2       3
(b d x  + 2 b c d x + b c )log(F)
+
2 4 4      2   3 3      2 2 2 2      2 3       2 4       2
(b d x  + 4 b c d x  + 6 b c d x  + 4 b c d x + b c )log(F)
+
6 6           5 5         2 4 4         3 3 3         4 2 2
2 b d x  + 12 b c d x  + 30 b c d x  + 40 b c d x  + 30 b c d x
+
5           6
12 b c d x + 2 b c
*
log(F)
+
8 8         7 7        2 6 6        3 5 5        4 4 4
6 d x  + 48 c d x  + 168 c d x  + 336 c d x  + 420 c d x
+
5 3 3        6 2 2       7         8
336 c d x  + 168 c d x  + 48 c d x + 6 c
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2
d x  + 2 c d x + c
%e
+
4      4         b log(F)        a log(F)
- b log(F) Ei(-------------------)%e
2 2              2
d x  + 2 c d x + c
/
48 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^5, x)
(122)
2 2 2      2         2 2       2
(b d x  + 2 b c d x + b c )log(F)
+
4 4          3 3        2 2 2        3         4             6 6
(b d x  + 4 b c d x  + 6 b c d x  + 4 b c d x + b c )log(F) + 2 d x
+
5 5       2 4 4       3 3 3       4 2 2       5         6
12 c d x  + 30 c d x  + 40 c d x  + 30 c d x  + 12 c d x + 2 c
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2
d x  + 2 c d x + c
%e
+
3      3         b log(F)        a log(F)
- b log(F) Ei(-------------------)%e
2 2              2
d x  + 2 c d x + c
/
12 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^3, x)
(123)
2 2                  2           4 4        3 3      2 2 2
(b d x  + 2 b c d x + b c )log(F) + d x  + 4 c d x  + 6 c d x
+
3       4
4 c d x + c
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2
d x  + 2 c d x + c
%e
+
2      2         b log(F)        a log(F)
- b log(F) Ei(-------------------)%e
2 2              2
d x  + 2 c d x + c
/
4 d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x), x)
(124)
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2
2 2              2            d x  + 2 c d x + c
(d x  + 2 c d x + c )%e
+
b log(F)        a log(F)
- b log(F)Ei(-------------------)%e
2 2              2
d x  + 2 c d x + c
/
2 d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x), x)
b log(F)        a log(F)
Ei(-------------------)%e
2 2              2
d x  + 2 c d x + c
(125)  - ---------------------------------
2 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^3, x)
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2
d x  + 2 c d x + c
%e
(126)  - ---------------------------------------
2 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^5, x)
(127)
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2
2 2              2            d x  + 2 c d x + c
(- b log(F) + d x  + 2 c d x + c )%e
-------------------------------------------------------------------------
2 3 2      2   2       2 2        2
(2 b d x  + 4 b c d x + 2 b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^7, x)
(128)
2      2         2 2                    2             4 4        3 3
- b log(F)  + (2 b d x  + 4 b c d x + 2 b c )log(F) - 2 d x  - 8 c d x
+
2 2 2      3         4
- 12 c d x  - 8 c d x - 2 c
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2
d x  + 2 c d x + c
%e
/
3 5 4      3   4 3       3 2 3 2      3 3 2       3 4        3
(2 b d x  + 8 b c d x  + 12 b c d x  + 8 b c d x + 2 b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (IN) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^9, x)
(129)
3      3       2 2 2      2           2 2       2
- b log(F)  + (3 b d x  + 6 b c d x + 3 b c )log(F)
+
4 4           3 3         2 2 2         3           4
(- 6 b d x  - 24 b c d x  - 36 b c d x  - 24 b c d x - 6 b c )log(F)
+
6 6         5 5       2 4 4        3 3 3       4 2 2       5         6
6 d x  + 36 c d x  + 90 c d x  + 120 c d x  + 90 c d x  + 36 c d x + 6 c
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2
d x  + 2 c d x + c
%e
/
4 7 6       4   6 5       4 2 5 4       4 3 4 3       4 4 3 2
2 b d x  + 12 b c d x  + 30 b c d x  + 40 b c d x  + 30 b c d x
+
4 5 2       4 6
12 b c d x + 2 b c d
*
4
log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^11, x)
(130)
4      4       3 2 2      3           3 2       3
- b log(F)  + (4 b d x  + 8 b c d x + 4 b c )log(F)
+
2 4 4       2   3 3       2 2 2 2       2 3          2 4       2
(- 12 b d x  - 48 b c d x  - 72 b c d x  - 48 b c d x - 12 b c )log(F)
+
6 6            5 5          2 4 4          3 3 3
24 b d x  + 144 b c d x  + 360 b c d x  + 480 b c d x
+
4 2 2          5            6
360 b c d x  + 144 b c d x + 24 b c
*
log(F)
+
8 8          7 7        2 6 6         3 5 5         4 4 4
- 24 d x  - 192 c d x  - 672 c d x  - 1344 c d x  - 1680 c d x
+
5 3 3        6 2 2        7          8
- 1344 c d x  - 672 c d x  - 192 c d x - 24 c
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2
d x  + 2 c d x + c
%e
/
5 9 8       5   8 7       5 2 7 6        5 3 6 5        5 4 5 4
2 b d x  + 16 b c d x  + 56 b c d x  + 112 b c d x  + 140 b c d x
+
5 5 4 3       5 6 3 2       5 7 2       5 8
112 b c d x  + 56 b c d x  + 16 b c d x + 2 b c d
*
5
log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.04 (EV) = 0.04 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^13, x)
(131)
5      5       4 2 2       4           4 2       4
- b log(F)  + (5 b d x  + 10 b c d x + 5 b c )log(F)
+
3 4 4       3   3 3        3 2 2 2       3 3          3 4
(- 20 b d x  - 80 b c d x  - 120 b c d x  - 80 b c d x - 20 b c )
*
3
log(F)
+
2 6 6        2   5 5        2 2 4 4         2 3 3 3
60 b d x  + 360 b c d x  + 900 b c d x  + 1200 b c d x
+
2 4 2 2        2 5          2 6
900 b c d x  + 360 b c d x + 60 b c
*
2
log(F)
+
8 8            7 7           2 6 6           3 5 5
- 120 b d x  - 960 b c d x  - 3360 b c d x  - 6720 b c d x
+
4 4 4           5 3 3           6 2 2          7
- 8400 b c d x  - 6720 b c d x  - 3360 b c d x  - 960 b c d x
+
8
- 120 b c
*
log(F)
+
10 10           9 9         2 8 8          3 7 7          4 6 6
120 d  x   + 1200 c d x  + 5400 c d x  + 14400 c d x  + 25200 c d x
+
5 5 5          6 4 4          7 3 3         8 2 2         9
30240 c d x  + 25200 c d x  + 14400 c d x  + 5400 c d x  + 1200 c d x
+
10
120 c
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2
d x  + 2 c d x + c
%e
/
6 11 10       6   10 9       6 2 9 8        6 3 8 7        6 4 7 6
2 b d  x   + 20 b c d  x  + 90 b c d x  + 240 b c d x  + 420 b c d x
+
6 5 6 5        6 6 5 4        6 7 4 3       6 8 3 2       6 9 2
504 b c d x  + 420 b c d x  + 240 b c d x  + 90 b c d x  + 20 b c d x
+
6 10
2 b c  d
*
6
log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.11 (EV) = 0.11 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^10, x)
(132)
+----------+
|  b log(F)
d |- --------
|      2
6      6 +---+  a log(F)     \|     d
- 32 b log(F) \|%pi %e        erf(--------------)
d x + c
+
5 2        5          5
(32 b d x + 32 b c d)log(F)
+
4 4 3       4   3 2       4 2 2        4 3        4
(16 b d x  + 48 b c d x  + 48 b c d x + 16 b c d)log(F)
+
3 6 5        3   5 4        3 2 4 3        3 3 3 2
24 b d x  + 120 b c d x  + 240 b c d x  + 240 b c d x
+
3 4 2        3 5
120 b c d x + 24 b c d
*
3
log(F)
+
2 8 7        2   7 6         2 2 6 5         2 3 5 4
60 b d x  + 420 b c d x  + 1260 b c d x  + 2100 b c d x
+
2 4 4 3         2 5 3 2        2 6 2        2 7
2100 b c d x  + 1260 b c d x  + 420 b c d x + 60 b c d
*
2
log(F)
+
10 9             9 8           2 8 7            3 7 6
210 b d  x  + 1890 b c d x  + 7560 b c d x  + 17640 b c d x
+
4 6 5            5 5 4            6 4 3           7 3 2
26460 b c d x  + 26460 b c d x  + 17640 b c d x  + 7560 b c d x
+
8 2           9
1890 b c d x + 210 b c d
*
log(F)
+
12 11            11 10          2 10 9           3 9 8
945 d  x   + 10395 c d  x   + 51975 c d  x  + 155925 c d x
+
4 8 7           5 7 6           6 6 5           7 5 4
311850 c d x  + 436590 c d x  + 436590 c d x  + 311850 c d x
+
8 4 3          9 3 2          10 2         11
155925 c d x  + 51975 c d x  + 10395 c  d x + 945 c  d
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
d x  + 2 c d x + c           |  b log(F)
%e                                      |- --------
|      2
\|     d
/
+----------+
2 |  b log(F)
10395 d  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^8, x)
(133)
+----------+
|  b log(F)
d |- --------
|      2
5      5 +---+  a log(F)     \|     d
- 16 b log(F) \|%pi %e        erf(--------------)
d x + c
+
4 2        4          4
(16 b d x + 16 b c d)log(F)
+
3 4 3       3   3 2       3 2 2       3 3        3
(8 b d x  + 24 b c d x  + 24 b c d x + 8 b c d)log(F)
+
2 6 5       2   5 4        2 2 4 3        2 3 3 2
12 b d x  + 60 b c d x  + 120 b c d x  + 120 b c d x
+
2 4 2        2 5
60 b c d x + 12 b c d
*
2
log(F)
+
8 7            7 6          2 6 5           3 5 4
30 b d x  + 210 b c d x  + 630 b c d x  + 1050 b c d x
+
4 4 3          5 3 2          6 2          7
1050 b c d x  + 630 b c d x  + 210 b c d x + 30 b c d
*
log(F)
+
10 9          9 8         2 8 7         3 7 6          4 6 5
105 d  x  + 945 c d x  + 3780 c d x  + 8820 c d x  + 13230 c d x
+
5 5 4         6 4 3         7 3 2        8 2         9
13230 c d x  + 8820 c d x  + 3780 c d x  + 945 c d x + 105 c d
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
d x  + 2 c d x + c           |  b log(F)
%e                                      |- --------
|      2
\|     d
/
+----------+
2 |  b log(F)
945 d  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^6, x)
(134)
+----------+
|  b log(F)
d |- --------
|      2
4      4 +---+  a log(F)     \|     d
- 8 b log(F) \|%pi %e        erf(--------------)
d x + c
+
3 2       3          3
(8 b d x + 8 b c d)log(F)
+
2 4 3       2   3 2       2 2 2       2 3        2
(4 b d x  + 12 b c d x  + 12 b c d x + 4 b c d)log(F)
+
6 5           5 4         2 4 3         3 3 2         4 2
6 b d x  + 30 b c d x  + 60 b c d x  + 60 b c d x  + 30 b c d x
+
5
6 b c d
*
log(F)
+
8 7          7 6        2 6 5        3 5 4        4 4 3
15 d x  + 105 c d x  + 315 c d x  + 525 c d x  + 525 c d x
+
5 3 2        6 2        7
315 c d x  + 105 c d x + 15 c d
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
d x  + 2 c d x + c           |  b log(F)
%e                                      |- --------
|      2
\|     d
/
+----------+
2 |  b log(F)
105 d  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^4, x)
(135)
+----------+
|  b log(F)
d |- --------
|      2
3      3 +---+  a log(F)     \|     d
- 4 b log(F) \|%pi %e        erf(--------------)
d x + c
+
2 2       2          2
(4 b d x + 4 b c d)log(F)
+
4 3          3 2        2 2         3              6 5
(2 b d x  + 6 b c d x  + 6 b c d x + 2 b c d)log(F) + 3 d x
+
5 4       2 4 3       3 3 2       4 2       5
15 c d x  + 30 c d x  + 30 c d x  + 15 c d x + 3 c d
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
d x  + 2 c d x + c           |  b log(F)
%e                                      |- --------
|      2
\|     d
/
+----------+
2 |  b log(F)
15 d  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^2, x)
(136)
+----------+
|  b log(F)
d |- --------
|      2
2      2 +---+  a log(F)     \|     d
- 2 b log(F) \|%pi %e        erf(--------------)
d x + c
+
2                      4 3        3 2      2 2     3
((2 b d x + 2 b c d)log(F) + d x  + 3 c d x  + 3 c d x + c d)
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
d x  + 2 c d x + c           |  b log(F)
%e                                      |- --------
|      2
\|     d
/
+----------+
2 |  b log(F)
3 d  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2), x)
(137)
+----------+
|  b log(F)
d |- --------
|      2
+---+  a log(F)     \|     d
- b log(F)\|%pi %e        erf(--------------)
d x + c
+
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
2                   d x  + 2 c d x + c           |  b log(F)
(d x + c d)%e                                      |- --------
|      2
\|     d
/
+----------+
2 |  b log(F)
d  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^2, x)
+----------+
|  b log(F)
d |- --------
|      2
+---+  a log(F)     \|     d
\|%pi %e        erf(--------------)
d x + c
(138)  - -----------------------------------
+----------+
2 |  b log(F)
2 d  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^4, x)
(139)
+----------+
|  b log(F)
d |- --------
|      2
+---+  a log(F)     \|     d
(d x + c)\|%pi %e        erf(--------------)
d x + c
+
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
d x  + 2 c d x + c           |  b log(F)
- 2 d %e                                      |- --------
|      2
\|     d
/
+----------+
3           2        |  b log(F)
(4 b d x + 4 b c d )log(F) |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^6, x)
(140)
+----------+
|  b log(F)
d |- --------
|      2
3 3        2 2      2         3  +---+  a log(F)     \|     d
(- 3 d x  - 9 c d x  - 9 c d x - 3 c )\|%pi %e        erf(--------------)
d x + c
+
3 2         2       2
(- 4 b d log(F) + 6 d x  + 12 c d x + 6 c d)
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
d x  + 2 c d x + c           |  b log(F)
%e                                      |- --------
|      2
\|     d
/
+----------+
2 5 3       2   4 2       2 2 3       2 3 2       2 |  b log(F)
(8 b d x  + 24 b c d x  + 24 b c d x + 8 b c d )log(F)  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^8, x)
(141)
5 5         4 4        2 3 3        3 2 2       4          5
(15 d x  + 75 c d x  + 150 c d x  + 150 c d x  + 75 c d x + 15 c )
*
+----------+
|  b log(F)
d |- --------
|      2
+---+  a log(F)     \|     d
\|%pi %e        erf(--------------)
d x + c
+
2        2          3 2           2          2               5 4
- 8 b d log(F)  + (20 b d x  + 40 b c d x + 20 b c d)log(F) - 30 d x
+
4 3        2 3 2        3 2        4
- 120 c d x  - 180 c d x  - 120 c d x - 30 c d
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
d x  + 2 c d x + c           |  b log(F)
%e                                      |- --------
|      2
\|     d
/
3 7 5       3   6 4        3 2 5 3        3 3 4 2       3 4 3
16 b d x  + 80 b c d x  + 160 b c d x  + 160 b c d x  + 80 b c d x
+
3 5 2
16 b c d
*
+----------+
3 |  b log(F)
log(F)  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) = 0.03 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^10, x)
(142)
7 7          6 6         2 5 5         3 4 4         4 3 3
- 105 d x  - 735 c d x  - 2205 c d x  - 3675 c d x  - 3675 c d x
+
5 2 2        6           7
- 2205 c d x  - 735 c d x - 105 c
*
+----------+
|  b log(F)
d |- --------
|      2
+---+  a log(F)     \|     d
\|%pi %e        erf(--------------)
d x + c
+
3        3        2 3 2        2   2        2 2        2
- 16 b d log(F)  + (56 b d x  + 112 b c d x + 56 b c d)log(F)
+
5 4            4 3          2 3 2          3 2
- 140 b d x  - 560 b c d x  - 840 b c d x  - 560 b c d x
+
4
- 140 b c d
*
log(F)
+
7 6           6 5         2 5 4         3 4 3         4 3 2
210 d x  + 1260 c d x  + 3150 c d x  + 4200 c d x  + 3150 c d x
+
5 2         6
1260 c d x + 210 c d
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
d x  + 2 c d x + c           |  b log(F)
%e                                      |- --------
|      2
\|     d
/
4 9 7        4   8 6        4 2 7 5         4 3 6 4         4 4 5 3
32 b d x  + 224 b c d x  + 672 b c d x  + 1120 b c d x  + 1120 b c d x
+
4 5 4 2        4 6 3        4 7 2
672 b c d x  + 224 b c d x + 32 b c d
*
+----------+
4 |  b log(F)
log(F)  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.04 (EV) = 0.04 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^12, x)
(143)
9 9           8 8          2 7 7          3 6 6           4 5 5
945 d x  + 8505 c d x  + 34020 c d x  + 79380 c d x  + 119070 c d x
+
5 4 4          6 3 3          7 2 2         8           9
119070 c d x  + 79380 c d x  + 34020 c d x  + 8505 c d x + 945 c
*
+----------+
|  b log(F)
d |- --------
|      2
+---+  a log(F)     \|     d
\|%pi %e        erf(--------------)
d x + c
+
4        4         3 3 2        3   2         3 2        3
- 32 b d log(F)  + (144 b d x  + 288 b c d x + 144 b c d)log(F)
+
2 5 4         2   4 3         2 2 3 2         2 3 2
- 504 b d x  - 2016 b c d x  - 3024 b c d x  - 2016 b c d x
+
2 4
- 504 b c d
*
2
log(F)
+
7 6             6 5            2 5 4            3 4 3
1260 b d x  + 7560 b c d x  + 18900 b c d x  + 25200 b c d x
+
4 3 2           5 2            6
18900 b c d x  + 7560 b c d x + 1260 b c d
*
log(F)
+
9 8            8 7          2 7 6           3 6 5
- 1890 d x  - 15120 c d x  - 52920 c d x  - 105840 c d x
+
4 5 4           5 4 3          6 3 2          7 2          8
- 132300 c d x  - 105840 c d x  - 52920 c d x  - 15120 c d x - 1890 c d
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
d x  + 2 c d x + c           |  b log(F)
%e                                      |- --------
|      2
\|     d
/
5 11 9        5   10 8         5 2 9 7         5 3 8 6
64 b d  x  + 576 b c d  x  + 2304 b c d x  + 5376 b c d x
+
5 4 7 5         5 5 6 4         5 6 5 3         5 7 4 2
8064 b c d x  + 8064 b c d x  + 5376 b c d x  + 2304 b c d x
+
5 8 3        5 9 2
576 b c d x + 64 b c d
*
+----------+
5 |  b log(F)
log(F)  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.07 (EV) = 0.07 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^14, x)
(144)
11 11             10 10           2 9 9            3 8 8
- 10395 d  x   - 114345 c d  x   - 571725 c d x  - 1715175 c d x
+
4 7 7            5 6 6            6 5 5            7 4 4
- 3430350 c d x  - 4802490 c d x  - 4802490 c d x  - 3430350 c d x
+
8 3 3           9 2 2           10             11
- 1715175 c d x  - 571725 c d x  - 114345 c  d x - 10395 c
*
+----------+
|  b log(F)
d |- --------
|      2
+---+  a log(F)     \|     d
\|%pi %e        erf(--------------)
d x + c
+
5        5         4 3 2        4   2         4 2        4
- 64 b d log(F)  + (352 b d x  + 704 b c d x + 352 b c d)log(F)
+
3 5 4         3   4 3         3 2 3 2         3 3 2
- 1584 b d x  - 6336 b c d x  - 9504 b c d x  - 6336 b c d x
+
3 4
- 1584 b c d
*
3
log(F)
+
2 7 6          2   6 5          2 2 5 4           2 3 4 3
5544 b d x  + 33264 b c d x  + 83160 b c d x  + 110880 b c d x
+
2 4 3 2          2 5 2          2 6
83160 b c d x  + 33264 b c d x + 5544 b c d
*
2
log(F)
+
9 8               8 7             2 7 6
- 13860 b d x  - 110880 b c d x  - 388080 b c d x
+
3 6 5             4 5 4             5 4 3
- 776160 b c d x  - 970200 b c d x  - 776160 b c d x
+
6 3 2             7 2             8
- 388080 b c d x  - 110880 b c d x - 13860 b c d
*
log(F)
+
11 10             10 9           2 9 8            3 8 7
20790 d  x   + 207900 c d  x  + 935550 c d x  + 2494800 c d x
+
4 7 6            5 6 5            6 5 4            7 4 3
4365900 c d x  + 5239080 c d x  + 4365900 c d x  + 2494800 c d x
+
8 3 2           9 2           10
935550 c d x  + 207900 c d x + 20790 c  d
*
2 2                  2
(a d x  + 2 a c d x + a c  + b)log(F)
-------------------------------------
2 2              2          +----------+
d x  + 2 c d x + c           |  b log(F)
%e                                      |- --------
|      2
\|     d
/
6 13 11         6   12 10         6 2 11 9          6 3 10 8
128 b d  x   + 1408 b c d  x   + 7040 b c d  x  + 21120 b c d  x
+
6 4 9 7          6 5 8 6          6 6 7 5          6 7 6 4
42240 b c d x  + 59136 b c d x  + 59136 b c d x  + 42240 b c d x
+
6 8 5 3         6 9 4 2         6 10 3         6 11 2
21120 b c d x  + 7040 b c d x  + 1408 b c  d x + 128 b c  d
*
+----------+
6 |  b log(F)
log(F)  |- --------
|      2
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.06 (EV) = 0.06 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^m, x)
3   3       2     2           2       3
%A a d  + 3 %A a c d  + 3 %A a c d + a c  + b
---------------------------------------------
x          3 3       2   2         2     3
++         %A d  + 3 %A c d  + 3 %A c d + c                 m
(145)   |   F                                             (%A d + c) d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^14, x)
(146)
4 3 3      4   2 2      4 2       4 3       4
(b d x  + 3 b c d x  + 3 b c d x + b c )log(F)
+
3 6 6      3   5 5       3 2 4 4       3 3 3 3       3 4 2 2
b d x  + 6 b c d x  + 15 b c d x  + 20 b c d x  + 15 b c d x
+
3 5       3 6
6 b c d x + b c
*
3
log(F)
+
2 9 9       2   8 8       2 2 7 7        2 3 6 6
2 b d x  + 18 b c d x  + 72 b c d x  + 168 b c d x
+
2 4 5 5        2 5 4 4        2 6 3 3       2 7 2 2
252 b c d x  + 252 b c d x  + 168 b c d x  + 72 b c d x
+
2 8         2 9
18 b c d x + 2 b c
*
2
log(F)
+
12 12           11 11          2 10 10           3 9 9
6 b d  x   + 72 b c d  x   + 396 b c d  x   + 1320 b c d x
+
4 8 8           5 7 7           6 6 6           7 5 5
2970 b c d x  + 4752 b c d x  + 5544 b c d x  + 4752 b c d x
+
8 4 4           9 3 3          10 2 2         11
2970 b c d x  + 1320 b c d x  + 396 b c  d x  + 72 b c  d x
+
12
6 b c
*
log(F)
+
15 15          14 14         2 13 13          3 12 12
24 d  x   + 360 c d  x   + 2520 c d  x   + 10920 c d  x
+
4 11 11          5 10 10           6 9 9           7 8 8
32760 c d  x   + 72072 c d  x   + 120120 c d x  + 154440 c d x
+
8 7 7           9 6 6          10 5 5          11 4 4
154440 c d x  + 120120 c d x  + 72072 c  d x  + 32760 c  d x
+
12 3 3         13 2 2        14          15
10920 c  d x  + 2520 c  d x  + 360 c  d x + 24 c
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
+
5      5              b log(F)              a log(F)
- b log(F) Ei(------------------------------)%e
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
360 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) = 0.03 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^11, x)
(147)
3 3 3      3   2 2      3 2       3 3       3
(b d x  + 3 b c d x  + 3 b c d x + b c )log(F)
+
2 6 6      2   5 5       2 2 4 4       2 3 3 3       2 4 2 2
b d x  + 6 b c d x  + 15 b c d x  + 20 b c d x  + 15 b c d x
+
2 5       2 6
6 b c d x + b c
*
2
log(F)
+
9 9           8 8         2 7 7          3 6 6
2 b d x  + 18 b c d x  + 72 b c d x  + 168 b c d x
+
4 5 5          5 4 4          6 3 3         7 2 2
252 b c d x  + 252 b c d x  + 168 b c d x  + 72 b c d x
+
8           9
18 b c d x + 2 b c
*
log(F)
+
12 12         11 11        2 10 10         3 9 9         4 8 8
6 d  x   + 72 c d  x   + 396 c d  x   + 1320 c d x  + 2970 c d x
+
5 7 7         6 6 6         7 5 5         8 4 4         9 3 3
4752 c d x  + 5544 c d x  + 4752 c d x  + 2970 c d x  + 1320 c d x
+
10 2 2       11         12
396 c  d x  + 72 c  d x + 6 c
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
+
4      4              b log(F)              a log(F)
- b log(F) Ei(------------------------------)%e
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
72 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.04 (EV) = 0.04 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^8, x)
(148)
2 3 3      2   2 2      2 2       2 3       2
(b d x  + 3 b c d x  + 3 b c d x + b c )log(F)
+
6 6          5 5         2 4 4         3 3 3         4 2 2
b d x  + 6 b c d x  + 15 b c d x  + 20 b c d x  + 15 b c d x
+
5         6
6 b c d x + b c
*
log(F)
+
9 9         8 8       2 7 7        3 6 6        4 5 5        5 4 4
2 d x  + 18 c d x  + 72 c d x  + 168 c d x  + 252 c d x  + 252 c d x
+
6 3 3       7 2 2       8         9
168 c d x  + 72 c d x  + 18 c d x + 2 c
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
+
3      3              b log(F)              a log(F)
- b log(F) Ei(------------------------------)%e
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
18 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^5, x)
(149)
3 3          2 2        2         3           6 6        5 5
(b d x  + 3 b c d x  + 3 b c d x + b c )log(F) + d x  + 6 c d x
+
2 4 4       3 3 3       4 2 2      5       6
15 c d x  + 20 c d x  + 15 c d x  + 6 c d x + c
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
+
2      2              b log(F)              a log(F)
- b log(F) Ei(------------------------------)%e
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
6 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^2, x)
(150)
3 3        2 2      2       3
(d x  + 3 c d x  + 3 c d x + c )
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
+
b log(F)              a log(F)
- b log(F)Ei(------------------------------)%e
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
3 d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x), x)
b log(F)              a log(F)
Ei(------------------------------)%e
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
(151)  - --------------------------------------------
3 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^4, x)
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
(152)  - ----------------------------------------------------
3 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^7, x)
(153)
3 3        2 2      2       3
(- b log(F) + d x  + 3 c d x  + 3 c d x + c )
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
/
2 4 3      2   3 2      2 2 2       2 3        2
(3 b d x  + 9 b c d x  + 9 b c d x + 3 b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^10, x)
(154)
2      2         3 3          2 2        2           3
- b log(F)  + (2 b d x  + 6 b c d x  + 6 b c d x + 2 b c )log(F)
+
6 6         5 5       2 4 4       3 3 3       4 2 2       5
- 2 d x  - 12 c d x  - 30 c d x  - 40 c d x  - 30 c d x  - 12 c d x
+
6
- 2 c
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
/
3 7 6       3   6 5       3 2 5 4       3 3 4 3       3 4 3 2
3 b d x  + 18 b c d x  + 45 b c d x  + 60 b c d x  + 45 b c d x
+
3 5 2       3 6
18 b c d x + 3 b c d
*
3
log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^13, x)
(155)
3      3       2 3 3      2   2 2      2 2         2 3       2
- b log(F)  + (3 b d x  + 9 b c d x  + 9 b c d x + 3 b c )log(F)
+
6 6           5 5         2 4 4          3 3 3         4 2 2
- 6 b d x  - 36 b c d x  - 90 b c d x  - 120 b c d x  - 90 b c d x
+
5           6
- 36 b c d x - 6 b c
*
log(F)
+
9 9         8 8        2 7 7        3 6 6        4 5 5        5 4 4
6 d x  + 54 c d x  + 216 c d x  + 504 c d x  + 756 c d x  + 756 c d x
+
6 3 3        7 2 2       8         9
504 c d x  + 216 c d x  + 54 c d x + 6 c
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
/
4 10 9       4   9 8        4 2 8 7        4 3 7 6        4 4 6 5
3 b d  x  + 27 b c d x  + 108 b c d x  + 252 b c d x  + 378 b c d x
+
4 5 5 4        4 6 4 3        4 7 3 2       4 8 2       4 9
378 b c d x  + 252 b c d x  + 108 b c d x  + 27 b c d x + 3 b c d
*
4
log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.05 (EV) = 0.05 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^16, x)
(156)
4      4       3 3 3       3   2 2       3 2         3 3       3
- b log(F)  + (4 b d x  + 12 b c d x  + 12 b c d x + 4 b c )log(F)
+
2 6 6       2   5 5        2 2 4 4        2 3 3 3
- 12 b d x  - 72 b c d x  - 180 b c d x  - 240 b c d x
+
2 4 2 2       2 5          2 6
- 180 b c d x  - 72 b c d x - 12 b c
*
2
log(F)
+
9 9            8 8          2 7 7           3 6 6
24 b d x  + 216 b c d x  + 864 b c d x  + 2016 b c d x
+
4 5 5           5 4 4           6 3 3          7 2 2
3024 b c d x  + 3024 b c d x  + 2016 b c d x  + 864 b c d x
+
8            9
216 b c d x + 24 b c
*
log(F)
+
12 12          11 11         2 10 10         3 9 9          4 8 8
- 24 d  x   - 288 c d  x   - 1584 c d  x   - 5280 c d x  - 11880 c d x
+
5 7 7          6 6 6          7 5 5          8 4 4
- 19008 c d x  - 22176 c d x  - 19008 c d x  - 11880 c d x
+
9 3 3         10 2 2        11          12
- 5280 c d x  - 1584 c  d x  - 288 c  d x - 24 c
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
/
5 13 12       5   12 11        5 2 11 10        5 3 10 9
3 b d  x   + 36 b c d  x   + 198 b c d  x   + 660 b c d  x
+
5 4 9 8         5 5 8 7         5 6 7 6         5 7 6 5
1485 b c d x  + 2376 b c d x  + 2772 b c d x  + 2376 b c d x
+
5 8 5 4        5 9 4 3        5 10 3 2       5 11 2       5 12
1485 b c d x  + 660 b c d x  + 198 b c  d x  + 36 b c  d x + 3 b c  d
*
5
log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.09 (EV) = 0.09 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^19, x)
(157)
5      5       4 3 3       4   2 2       4 2         4 3       4
- b log(F)  + (5 b d x  + 15 b c d x  + 15 b c d x + 5 b c )log(F)
+
3 6 6        3   5 5        3 2 4 4        3 3 3 3
- 20 b d x  - 120 b c d x  - 300 b c d x  - 400 b c d x
+
3 4 2 2        3 5          3 6
- 300 b c d x  - 120 b c d x - 20 b c
*
3
log(F)
+
2 9 9        2   8 8         2 2 7 7         2 3 6 6
60 b d x  + 540 b c d x  + 2160 b c d x  + 5040 b c d x
+
2 4 5 5         2 5 4 4         2 6 3 3         2 7 2 2
7560 b c d x  + 7560 b c d x  + 5040 b c d x  + 2160 b c d x
+
2 8          2 9
540 b c d x + 60 b c
*
2
log(F)
+
12 12             11 11           2 10 10            3 9 9
- 120 b d  x   - 1440 b c d  x   - 7920 b c d  x   - 26400 b c d x
+
4 8 8            5 7 7             6 6 6
- 59400 b c d x  - 95040 b c d x  - 110880 b c d x
+
7 5 5            8 4 4            9 3 3           10 2 2
- 95040 b c d x  - 59400 b c d x  - 26400 b c d x  - 7920 b c  d x
+
11             12
- 1440 b c  d x - 120 b c
*
log(F)
+
15 15           14 14          2 13 13          3 12 12
120 d  x   + 1800 c d  x   + 12600 c d  x   + 54600 c d  x
+
4 11 11           5 10 10           6 9 9           7 8 8
163800 c d  x   + 360360 c d  x   + 600600 c d x  + 772200 c d x
+
8 7 7           9 6 6           10 5 5           11 4 4
772200 c d x  + 600600 c d x  + 360360 c  d x  + 163800 c  d x
+
12 3 3          13 2 2         14           15
54600 c  d x  + 12600 c  d x  + 1800 c  d x + 120 c
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
/
6 16 15       6   15 14        6 2 14 13         6 3 13 12
3 b d  x   + 45 b c d  x   + 315 b c d  x   + 1365 b c d  x
+
6 4 12 11         6 5 11 10          6 6 10 9          6 7 9 8
4095 b c d  x   + 9009 b c d  x   + 15015 b c d  x  + 19305 b c d x
+
6 8 8 7          6 9 7 6         6 10 6 5         6 11 5 4
19305 b c d x  + 15015 b c d x  + 9009 b c  d x  + 4095 b c  d x
+
6 12 4 3        6 13 3 2       6 14 2       6 15
1365 b c  d x  + 315 b c  d x  + 45 b c  d x + 3 b c  d
*
6
log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.16 (EV) = 0.16 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^3, x)
(158)
3           2           6 4        5 3      2 4 2      3 3
(3 b d x + 3 b c d )log(F) + d x  + 4 c d x  + 6 c d x  + 4 c d x
+
4 2
c d
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3            +----------+2
d x  + 3 c d x  + 3 c d x + c             |  b log(F)
%e                                                    |- --------
3|      3
\|     d
+
2      2  a log(F)      2              b log(F)
3 b log(F) %e        Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
+----------+2
3  |  b log(F)
4 d   |- --------
3|      3
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x), x)
(159)
3 2        2     2
(d x  + 2 c d x + c d)
*
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3            +----------+
d x  + 3 c d x  + 3 c d x + c             |  b log(F)
%e                                                    |- --------
3|      3
\|     d
+
a log(F)      1              b log(F)
b log(F)%e        Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
+----------+
2  |  b log(F)
2 d   |- --------
3|      3
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x)^3), x)
(160)
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3
3       2             d x  + 3 c d x  + 3 c d x + c
(d x + c d )%e
*
+----------+2
|  b log(F)
|- --------
3|      3
\|     d
+
a log(F)      2              b log(F)
b log(F)%e        Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
+----------+2
3  |  b log(F)
d   |- --------
3|      3
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (IN) = 0.02 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^2, x)
a log(F)      1              b log(F)
%e        Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
(161)  ---------------------------------------------------
+----------+
2  |  b log(F)
3 d   |- --------
3|      3
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^3, x)
a log(F)      2              b log(F)
%e        Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
(162)  ---------------------------------------------------
+----------+2
3  |  b log(F)
3 d   |- --------
3|      3
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^5, x)
(163)
3 3          2 2        2         3
(a d x  + 3 a c d x  + 3 a c d x + a c  + b)log(F)
--------------------------------------------------
3 3        2 2      2       3            +----------+
d x  + 3 c d x  + 3 c d x + c             |  b log(F)
- 3 d %e                                                    |- --------
3|      3
\|     d
+
a log(F)      1              b log(F)
(- d x - c)%e        Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
+----------+
3           2         |  b log(F)
(9 b d x + 9 b c d )log(F)  |- --------
3|      3
\|     d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
-- n symbolic
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^m, x)
x                         n
++            m b (%A d + c)  + a
(164)   |   (%A d + c) F                 d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^3, x)
x                                                 n
++     3 3       2   2         2     3  b (%A d + c)  + a
(165)   |   (%A d  + 3 %A c d  + 3 %A c d + c )F                 d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^2, x)
x                                     n
++     2 2               2  b (%A d + c)  + a
(166)   |   (%A d  + 2 %A c d + c )F                 d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x), x)
x                        n
++             b (%A d + c)  + a
(167)   |   (%A d + c)F                 d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n), x)
x              n
++   b (%A d + c)  + a
(168)   |   F                 d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^n)/(c+d*x), x)
a log(F)             n log(d x + c)
%e        Ei(b log(F)%e              )
(169)  --------------------------------------
d n
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^2, x)
n
x    b (%A d + c)  + a
++    F
(170)   |   --------------------- d%A
++     2 2               2
%A d  + 2 %A c d + c
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^3, x)
n
x          b (%A d + c)  + a
++          F
(171)   |   --------------------------------- d%A
++     3 3       2   2         2     3
%A d  + 3 %A c d  + 3 %A c d + c
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^4, x)
n
x                b (%A d + c)  + a
++                F
(172)   |   --------------------------------------------- d%A
++     4 4       3   3       2 2 2         3     4
%A d  + 4 %A c d  + 6 %A c d  + 4 %A c d + c
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+6*n), x)
(173)
5      5   n log(d x + c) 5      4      4   n log(d x + c) 4
b log(F) (%e              )  - 5 b log(F) (%e              )
+
3      3   n log(d x + c) 3       2      2   n log(d x + c) 2
20 b log(F) (%e              )  - 60 b log(F) (%e              )
+
n log(d x + c)
120 b log(F)%e               - 120
*
n log(d x + c)
b log(F)%e               + a log(F)
%e
/
6          6
b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+5*n), x)
(174)
4      4   n log(d x + c) 4      3      3   n log(d x + c) 3
b log(F) (%e              )  - 4 b log(F) (%e              )
+
2      2   n log(d x + c) 2                n log(d x + c)
12 b log(F) (%e              )  - 24 b log(F)%e               + 24
*
n log(d x + c)
b log(F)%e               + a log(F)
%e
/
5          5
b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+4*n), x)
(175)
3      3   n log(d x + c) 3      2      2   n log(d x + c) 2
b log(F) (%e              )  - 3 b log(F) (%e              )
+
n log(d x + c)
6 b log(F)%e               - 6
*
n log(d x + c)
b log(F)%e               + a log(F)
%e
/
4          4
b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+3*n), x)
(176)
2      2   n log(d x + c) 2               n log(d x + c)
(b log(F) (%e              )  - 2 b log(F)%e               + 2)
*
n log(d x + c)
b log(F)%e               + a log(F)
%e
/
3          3
b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+2*n), x)
n log(d x + c)
n log(d x + c)       b log(F)%e               + a log(F)
(b log(F)%e               - 1)%e
(177)  -------------------------------------------------------------------
2          2
b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+n), x)
n log(d x + c)
b log(F)%e               + a log(F)
%e
(178)  -------------------------------------
b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)/(c+d*x), x)
a log(F)             n log(d x + c)
%e        Ei(b log(F)%e              )
(179)  --------------------------------------
d n
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-n), x)
(180)
n log(d x + c)
b log(F)%e               + a log(F)
- %e
+
a log(F)  n log(d x + c)             n log(d x + c)
b log(F)%e        %e              Ei(b log(F)%e              )
/
n log(d x + c)
d n %e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-2*n), x)
(181)
n log(d x + c)
n log(d x + c)       b log(F)%e               + a log(F)
(- b log(F)%e               - 1)%e
+
2      2  a log(F)   n log(d x + c) 2             n log(d x + c)
b log(F) %e        (%e              ) Ei(b log(F)%e              )
/
n log(d x + c) 2
2 d n (%e              )
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-3*n), x)
(182)
2      2   n log(d x + c) 2             n log(d x + c)
(- b log(F) (%e              )  - b log(F)%e               - 2)
*
n log(d x + c)
b log(F)%e               + a log(F)
%e
+
3      3  a log(F)   n log(d x + c) 3             n log(d x + c)
b log(F) %e        (%e              ) Ei(b log(F)%e              )
/
n log(d x + c) 3
6 d n (%e              )
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-4*n), x)
(183)
3      3   n log(d x + c) 3    2      2   n log(d x + c) 2
- b log(F) (%e              )  - b log(F) (%e              )
+
n log(d x + c)
- 2 b log(F)%e               - 6
*
n log(d x + c)
b log(F)%e               + a log(F)
%e
+
4      4  a log(F)   n log(d x + c) 4             n log(d x + c)
b log(F) %e        (%e              ) Ei(b log(F)%e              )
/
n log(d x + c) 4
24 d n (%e              )
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-5*n), x)
(184)
4      4   n log(d x + c) 4    3      3   n log(d x + c) 3
- b log(F) (%e              )  - b log(F) (%e              )
+
2      2   n log(d x + c) 2               n log(d x + c)
- 2 b log(F) (%e              )  - 6 b log(F)%e               - 24
*
n log(d x + c)
b log(F)%e               + a log(F)
%e
+
5      5  a log(F)   n log(d x + c) 5             n log(d x + c)
b log(F) %e        (%e              ) Ei(b log(F)%e              )
/
n log(d x + c) 5
120 d n (%e              )
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x)^n)*(a+b*x)^(-1+1/2*n), x)
(n - 2)log(b x + a)
-------------------
+---+                        2          +----------+
\|%pi erf((b x + a)%e                   \|- c log(F) )
(185)  ------------------------------------------------------
+----------+
b n\|- c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate((a+b*x)^(-1+1/2*n)/F^(c*(a+b*x)^n), x)
(n - 2)log(b x + a)
-------------------
+---+                        2          +--------+
\|%pi erf((b x + a)%e                   \|c log(F) )
(186)  ----------------------------------------------------
+--------+
b n\|c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- Integrands of the form (e+f x)^m F^(a+b (c+d x)^n)
-- n>0
integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^5, x)
(187)
3 5   5       3 4 2   4       3 3 3 2 3       3 2 4 3 2
- 4 b c d f  + 20 b c d e f  - 40 b c d e f  + 40 b c d e f
+
3   5 4       3 6 5
- 20 b c d e f + 4 b d e
*
3
log(F)
+
2 3   5       2 2 2   4       2   3 2 3       2 4 3 2       2
(20 b c d f  - 60 b c d e f  + 60 b c d e f  - 20 b d e f )log(F)
+
5         2   4
(- 15 b c d f  + 15 b d e f )log(F)
*
+------------+
|     2
+---+  a log(F)    (d x + c)\|- b d log(F)
\|%pi %e        erf(------------------------)
d
+
2 4 5 4         2   3 5       2 4   4  3
4 b d f x  + (- 4 b c d f  + 20 b d e f )x
+
2 2 2 5       2   3   4       2 4 2 3  2
(4 b c d f  - 20 b c d e f  + 40 b d e f )x
+
2 3   5       2 2 2   4       2   3 2 3       2 4 3 2
(- 4 b c d f  + 20 b c d e f  - 40 b c d e f  + 40 b d e f )x
+
2 4 5       2 3     4       2 2 2 2 3       2   3 3 2
4 b c f  - 20 b c d e f  + 40 b c d e f  - 40 b c d e f
+
2 4 4
20 b d e f
*
2
log(F)
+
2 5 2              5         2   4           2 5
- 8 b d f x  + (14 b c d f  - 30 b d e f )x - 18 b c f
+
4         2 2 3
50 b c d e f  - 40 b d e f
*
log(F)
+
5
8 f
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
+------------+
3 6      3 |     2
8 b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^4, x)
(188)
2 4   4       2 3 2   3       2 2 3 2 2       2   4 3
4 b c d f  - 16 b c d e f  + 24 b c d e f  - 16 b c d e f
+
2 5 4
4 b d e
*
2
log(F)
+
2   4           2   3         3 2 2               4
(- 12 b c d f  + 24 b c d e f  - 12 b d e f )log(F) + 3 d f
*
+------------+
|     2
+---+  a log(F)    (d x + c)\|- b d log(F)
\|%pi %e        erf(------------------------)
d
+
3 4 3             2 4         3   3  2
4 b d f x  + (- 4 b c d f  + 16 b d e f )x
+
2   4           2   3         3 2 2          3 4
(4 b c d f  - 16 b c d e f  + 24 b d e f )x - 4 b c f
+
2     3           2 2 2         3 3
16 b c d e f  - 24 b c d e f  + 16 b d e f
*
log(F)
+
4          4           3
- 6 d f x + 10 c f  - 16 d e f
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
+------------+
2 5      2 |     2
8 b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^3, x)
(189)
2 3   3      2 2 2   2      2   3 2       2 4 3       2
(- 2 b c d f  + 6 b c d e f  - 6 b c d e f + 2 b d e )log(F)
+
3        2   2
(3 b c d f  - 3 b d e f )log(F)
*
+------------+
|     2
+---+  a log(F)    (d x + c)\|- b d log(F)
\|%pi %e        erf(------------------------)
d
+
2 3 2               3        2   2          2 3
2 b d f x  + (- 2 b c d f  + 6 b d e f )x + 2 b c f
+
2        2 2
- 6 b c d e f  + 6 b d e f
*
log(F)
+
3
- 2 f
*
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
%e                                     \|- b d log(F)
/
+------------+
2 4      2 |     2
4 b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^2, x)
(190)
2   2          2           3 2             2  +---+  a log(F)
((2 b c d f  - 4 b c d e f + 2 b d e )log(F) - d f )\|%pi %e
*
+------------+
|     2
(d x + c)\|- b d log(F)
erf(------------------------)
d
+
2 2                  2
2         2             (b d x  + 2 b c d x + b c  + a)log(F)
(2 d f x - 2 c f  + 4 d e f)%e
*
+------------+
|     2
\|- b d log(F)
/
+------------+
3       |     2
4 b d log(F)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)*(e+f*x), x)
(191)
+------------+
|     2
2         +---+  a log(F)    (d x + c)\|- b d log(F)
(- b c d f + b d e)log(F)\|%pi %e        erf(------------------------)
d
+
2 2                  2            +------------+
(b d x  + 2 b c d x + b c  + a)log(F) |     2
f %e                                     \|- b d log(F)
/
+------------+
2       |     2
2 b d log(F)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2), x)
+------------+
|     2
+---+  a log(F)    (d x + c)\|- b d log(F)
\|%pi %e        erf(------------------------)
d
(192)  ---------------------------------------------
+------------+
|     2
2 \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(e+f*x), x)
2   2                   2
x  %A b d  + 2 %A b c d + b c  + a
++  F
(193)   |   -------------------------------- d%A
++               %A f + e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(e+f*x)^2, x)
2   2                   2
x  %A b d  + 2 %A b c d + b c  + a
++  F
(194)   |   -------------------------------- d%A
++           2 2               2
%A f  + 2 %A e f + e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(e+f*x)^3, x)
2   2                   2
x   %A b d  + 2 %A b c d + b c  + a
++   F
(195)   |   --------------------------------- d%A
++     3 3       2   2         2     3
%A f  + 3 %A e f  + 3 %A e f + e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e*(c+d*x)^3)*(a+b*x)^3, x)
(196)
3   3        2   2      2         3
3           2       3    d e x  + 3 c d e x  + 3 c d e x + c e
(3 b d x + 9 a b d - 6 b c)%e
*
+-----+2
3|   3
\|- d e
+
3 4      2     3        2 2 2      3 3       3
((- 3 a d  + 9 a b c d  - 9 a b c d  + 3 b c d)e + b d)
*
+-----+
1    3   3        2   2      2         3  3|   3
Gamma(-,- d e x  - 3 c d e x  - 3 c d e x - c e)\|- d e
3
+
2   4         2   3      3 2 2
(- 9 a b d  + 18 a b c d  - 9 b c d )e
*
2    3   3        2   2      2         3
Gamma(-,- d e x  - 3 c d e x  - 3 c d e x - c e)
3
/
+-----+2
4  3|   3
9 d e \|- d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e*(c+d*x)^3)*(a+b*x)^2, x)
(197)
3   3        2   2      2         3   +-----+2
2  d e x  + 3 c d e x  + 3 c d e x + c e 3|   3
b %e                                      \|- d e
+
2 3            2    2 2
(- a d  + 2 a b c d  - b c d)e
*
+-----+
1    3   3        2   2      2         3  3|   3
Gamma(-,- d e x  - 3 c d e x  - 3 c d e x - c e)\|- d e
3
+
3      2   2         2    3   3        2   2      2         3
(- 2 a b d  + 2 b c d )e Gamma(-,- d e x  - 3 c d e x  - 3 c d e x - c e)
3
/
+-----+2
3  3|   3
3 d e \|- d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(%e^(e*(c+d*x)^3)*(a+b*x), x)
(198)
+-----+
1    3   3        2   2      2         3  3|   3
(- a d + b c)Gamma(-,- d e x  - 3 c d e x  - 3 c d e x - c e)\|- d e
3
+
2    3   3        2   2      2         3
- b d Gamma(-,- d e x  - 3 c d e x  - 3 c d e x - c e)
3
/
+-----+2
3|   3
3 d \|- d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e*(c+d*x)^3), x)
1    3   3        2   2      2         3
Gamma(-,- d e x  - 3 c d e x  - 3 c d e x - c e)
3
(199)  - ------------------------------------------------
+-----+
3|   3
3 \|- d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e*(c+d*x)^3)/(a+b*x), x)
3 3       2   2         2     3
x   (%A d  + 3 %A c d  + 3 %A c d + c )e
++  %e
(200)   |   -------------------------------------- d%A
++                  %A b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e*(c+d*x)^3)/(a+b*x)^2, x)
3 3       2   2         2     3
x   (%A d  + 3 %A c d  + 3 %A c d + c )e
++  %e
(201)   |   -------------------------------------- d%A
++              2 2               2
%A b  + 2 %A a b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
-- n<0
integrate(F^(a+b/(c+d*x))/(e+f*x), x)
(202)
((a c + b)f - a d e)log(F)
--------------------------
(- b d f x - b d e)log(F)             c f - d e
Ei(----------------------------)%e
2       2
(c d f - d e)x + c f - c d e
+
b log(F)   a log(F)
- Ei(--------)%e
d x + c
/
f
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x))/(e+f*x)^2, x)
(203)
(- b d f x - b d e)log(F)
(- b d f x - b d e)log(F)Ei(----------------------------)
2       2
(c d f - d e)x + c f - c d e
*
((a c + b)f - a d e)log(F)
--------------------------
c f - d e
%e
+
(a d x + a c + b)log(F)
-----------------------
2       2                    d x + c
((- c d f + d e)x - c f + c d e)%e
/
2 3            2    2 2       2   2          2     2 3
(c f  - 2 c d e f  + d e f)x + c e f  - 2 c d e f + d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x))/(e+f*x)^3, x)
(204)
2 2 3 2      2 2   2     2 2 2        2
(b d f x  + 2 b d e f x + b d e f)log(F)
+
2 3        3   2  2           2   2        3 2
(2 b c d f  - 2 b d e f )x  + (4 b c d e f  - 4 b d e f)x
+
2 2         3 3
2 b c d e f - 2 b d e
*
log(F)
*
((a c + b)f - a d e)log(F)
--------------------------
(- b d f x - b d e)log(F)             c f - d e
Ei(----------------------------)%e
2       2
(c d f - d e)x + c f - c d e
+
2 3      3   2  2       2   3      3 2         2     2
(b c d f  - b d e f )x  + (b c d f  - b d e f)x + b c d e f
+
2 2
- b c d e f
*
log(F)
+
2 2 3        3   2    4 2   2       2 2   2        3 2       4 3
(c d f  - 2 c d e f  + d e f)x  + (2 c d e f  - 4 c d e f + 2 d e )x
+
4 3      3     2      2 2 2         3 3
- c f  + 4 c d e f  - 5 c d e f + 2 c d e
*
(a d x + a c + b)log(F)
-----------------------
d x + c
%e
/
4 6      3     5       2 2 2 4        3 3 3      4 4 2  2
(2 c f  - 8 c d e f  + 12 c d e f  - 8 c d e f  + 2 d e f )x
+
4   5       3   2 4       2 2 3 3         3 4 2      4 5
(4 c e f  - 16 c d e f  + 24 c d e f  - 16 c d e f  + 4 d e f)x
+
4 2 4      3   3 3       2 2 4 2        3 5       4 6
2 c e f  - 8 c d e f  + 12 c d e f  - 8 c d e f + 2 d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x))/(e+f*x)^4, x)
(205)
3 3 5 3      3 3   4 2      3 3 2 3     3 3 3 2       3
(- b d f x  - 3 b d e f x  - 3 b d e f x - b d e f )log(F)
+
2   3 5      2 4   4  3          2   3   4       2 4 2 3  2
(- 6 b c d f  + 6 b d e f )x  + (- 18 b c d e f  + 18 b d e f )x
+
2   3 2 3       2 4 3 2        2   3 3 2      2 4 4
(- 18 b c d e f  + 18 b d e f )x - 6 b c d e f  + 6 b d e f
*
2
log(F)
+
2 3 5           4   4        5 2 3  3
(- 6 b c d f  + 12 b c d e f  - 6 b d e f )x
+
2 3   4           4 2 3         5 3 2  2
(- 18 b c d e f  + 36 b c d e f  - 18 b d e f )x
+
2 3 2 3           4 3 2         5 4           2 3 3 2
(- 18 b c d e f  + 36 b c d e f  - 18 b d e f)x - 6 b c d e f
+
4 4         5 5
12 b c d e f - 6 b d e
*
log(F)
*
((a c + b)f - a d e)log(F)
--------------------------
(- b d f x - b d e)log(F)             c f - d e
Ei(----------------------------)%e
2       2
(c d f - d e)x + c f - c d e
+
2   3 5    2 4   4  3
(- b c d f  + b d e f )x
+
2 2 2 5    2   3   4      2 4 2 3  2
(- b c d f  - b c d e f  + 2 b d e f )x
+
2 2 2   4    2   3 2 3    2 4 3 2      2 2 2 2 3    2   3 3 2
(- 2 b c d e f  + b c d e f  + b d e f )x - b c d e f  + b c d e f
*
2
log(F)
+
2 3 5           4   4        5 2 3  3
(- 5 b c d f  + 10 b c d e f  - 5 b d e f )x
+
3 2 5        2 3   4           4 2 3         5 3 2  2
(- 4 b c d f  - 3 b c d e f  + 18 b c d e f  - 11 b d e f )x
+
4   5         3 2   4         2 3 2 3          4 3 2
b c d f  - 12 b c d e f  + 15 b c d e f  + 2 b c d e f
+
5 4
- 6 b d e f
*
x
+
4     4        3 2 2 3         2 3 3 2          4 4
b c d e f  - 8 b c d e f  + 13 b c d e f  - 6 b c d e f
*
log(F)
+
3 3 5      2 4   4        5 2 3      6 3 2  3
(- 2 c d f  + 6 c d e f  - 6 c d e f  + 2 d e f )x
+
3 3   4       2 4 2 3         5 3 2      6 4   2
(- 6 c d e f  + 18 c d e f  - 18 c d e f  + 6 d e f)x
+
3 3 2 3       2 4 3 2         5 4       6 5        6 5
(- 6 c d e f  + 18 c d e f  - 18 c d e f + 6 d e )x - 2 c f
+
5     4       4 2 2 3       3 3 3 2       2 4 4         5 5
12 c d e f  - 30 c d e f  + 38 c d e f  - 24 c d e f + 6 c d e
*
(a d x + a c + b)log(F)
-----------------------
d x + c
%e
/
6 9       5     8       4 2 2 7        3 3 3 6       2 4 4 5
6 c f  - 36 c d e f  + 90 c d e f  - 120 c d e f  + 90 c d e f
+
5 5 4      6 6 3
- 36 c d e f  + 6 d e f
*
3
x
+
6   8        5   2 7        4 2 3 6        3 3 4 5        2 4 5 4
18 c e f  - 108 c d e f  + 270 c d e f  - 360 c d e f  + 270 c d e f
+
5 6 3       6 7 2
- 108 c d e f  + 18 d e f
*
2
x
+
6 2 7        5   3 6        4 2 4 5        3 3 5 4        2 4 6 3
18 c e f  - 108 c d e f  + 270 c d e f  - 360 c d e f  + 270 c d e f
+
5 7 2       6 8
- 108 c d e f  + 18 d e f
*
x
+
6 3 6       5   4 5       4 2 5 4        3 3 6 3       2 4 7 2
6 c e f  - 36 c d e f  + 90 c d e f  - 120 c d e f  + 90 c d e f
+
5 8       6 9
- 36 c d e f + 6 d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.03 (EV) = 0.04 sec
integrate(%e^(e/(c+d*x))*(a+b*x)^4, x)
(206)
4 5 5       4 4           3 5  4
24 b d x  + (6 b d e + 120 a b d )x
+
4 3 2          3 4       4   3          2 2 5  3
(2 b d e  + (40 a b d  - 16 b c d )e + 240 a b d )x
+
4 2 3          3 3       4   2  2
b d e  + (20 a b d  - 14 b c d )e
+
2 2 4          3   3       4 2 2          3   5
(120 a b d  - 120 a b c d  + 36 b c d )e + 240 a b d
*
2
x
+
4   4          3 2       4     3
b d e  + (20 a b d  - 18 b c d)e
+
2 2 3          3   2       4 2   2
(120 a b d  - 200 a b c d  + 86 b c d)e
+
3   4        2 2   3          3 2 2       4 3           4 5
(240 a b d  - 480 a b c d  + 360 a b c d  - 96 b c d)e + 120 a d
*
x
+
4   4          3          4 2  3
b c e  + (20 a b c d - 19 b c )e
+
2 2   2          3 2         4 3  2
(120 a b c d  - 220 a b c d + 102 b c )e
+
3     3        2 2 2 2          3 3         4 4          4   4
(240 a b c d  - 600 a b c d  + 520 a b c d - 154 b c )e + 120 a c d
+
3   2 3        2 2 3 2          3 4        4 5
- 240 a b c d  + 240 a b c d  - 120 a b c d + 24 b c
*
e
-------
d x + c
%e
+
4 5            3        4   4
- b e  + (- 20 a b d + 20 b c)e
+
2 2 2          3           4 2  3
(- 120 a b d  + 240 a b c d - 120 b c )e
+
3   3        2 2   2          3 2         4 3  2
(- 240 a b d  + 720 a b c d  - 720 a b c d + 240 b c )e
+
4 4        3     3        2 2 2 2          3 3         4 4
(- 120 a d  + 480 a b c d  - 720 a b c d  + 480 a b c d - 120 b c )e
*
e
Ei(-------)
d x + c
/
5
120 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) = 0.03 sec
integrate(%e^(e/(c+d*x))*(a+b*x)^3, x)
(207)
3 4 4       3 3          2 4  3
6 b d x  + (2 b d e + 24 a b d )x
+
3 2 2          2 3      3   2         2   4  2
(b d e  + (12 a b d  - 6 b c d )e + 36 a b d )x
+
3   3          2 2       3     2
b d e  + (12 a b d  - 10 b c d)e
+
2   3         2   2       3 2          3 4
(36 a b d  - 48 a b c d  + 18 b c d)e + 24 a d
*
x
+
3   3          2          3 2  2
b c e  + (12 a b c d - 11 b c )e
+
2     2         2 2        3 3         3   3       2   2 2
(36 a b c d  - 60 a b c d + 26 b c )e + 24 a c d  - 36 a b c d
+
2 3       3 4
24 a b c d - 6 b c
*
e
-------
d x + c
%e
+
3 4            2        3   3
- b e  + (- 12 a b d + 12 b c)e
+
2   2         2          3 2  2
(- 36 a b d  + 72 a b c d - 36 b c )e
+
3 3       2     2         2 2        3 3
(- 24 a d  + 72 a b c d  - 72 a b c d + 24 b c )e
*
e
Ei(-------)
d x + c
/
4
24 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x))*(a+b*x)^2, x)
(208)
2 3 3     2 2           3  2
2 b d x  + (b d e + 6 a b d )x
+
2   2           2      2           2 3      2   2
(b d e  + (6 a b d  - 4 b c d)e + 6 a d )x + b c e
+
2 2        2   2          2       2 3
(6 a b c d - 5 b c )e + 6 a c d  - 6 a b c d + 2 b c
*
e
-------
d x + c
%e
+
2 3                   2   2         2 2                   2 2
(- b e  + (- 6 a b d + 6 b c)e  + (- 6 a d  + 12 a b c d - 6 b c )e)
*
e
Ei(-------)
d x + c
/
3
6 d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e/(c+d*x))*(a+b*x), x)
(209)
e
-------
2 2                 2                          2   d x + c
(b d x  + (b d e + 2 a d )x + b c e + 2 a c d - b c )%e
+
2                            e
(- b e  + (- 2 a d + 2 b c)e)Ei(-------)
d x + c
/
2
2 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)), x)
e
-------
d x + c           e
(d x + c)%e        - e Ei(-------)
d x + c
(210)  ----------------------------------
d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e/(c+d*x))/(a+b*x), x)
b e
- ---------
b d e x + a d e            a d - b c         e
Ei(------------------------------)%e            - Ei(-------)
2                        2                    d x + c
(a d  - b c d)x + a c d - b c
(211)  -------------------------------------------------------------
b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x))/(a+b*x)^2, x)
(212)
e
-------
2                        2   d x + c
((a d  - b c d)x + a c d - b c )%e
+
b e
- ---------
b d e x + a d e            a d - b c
(- b d e x - a d e)Ei(------------------------------)%e
2                        2
(a d  - b c d)x + a c d - b c
/
2   2        2       3 2      3 2      2           2 2
(a b d  - 2 a b c d + b c )x + a d  - 2 a b c d + a b c
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e/(c+d*x))/(a+b*x)^3, x)
(213)
2 3    3   2      2   4        2   3    3 2 2  2
((- a b d  + b c d )e + a b d  - 2 a b c d  + b c d )x
+
2   3    3 2         3 4      2     3        2 2 2
((- a b d  + b c d)e + 2 a d  - 4 a b c d  + 2 a b c d )x
+
2     2      2 2         3   3      2   2 2        2 3     3 4
(- a b c d  + a b c d)e + 2 a c d  - 5 a b c d  + 4 a b c d - b c
*
e
-------
d x + c
%e
+
3 2 2           2 3      3   2    2
(b d e  + (- 2 a b d  + 2 b c d )e)x
+
2 2 2         2   3        2   2        2   2 2
(2 a b d e  + (- 4 a b d  + 4 a b c d )e)x + a b d e
+
3 3      2     2
(- 2 a d  + 2 a b c d )e
*
b e
- ---------
b d e x + a d e            a d - b c
Ei(------------------------------)%e
2                        2
(a d  - b c d)x + a c d - b c
/
4 2 4      3 3   3       2 4 2 2        5 3       6 4  2
(2 a b d  - 8 a b c d  + 12 a b c d  - 8 a b c d + 2 b c )x
+
5   4       4 2   3       3 3 2 2       2 4 3         5 4        6 4
(4 a b d  - 16 a b c d  + 24 a b c d  - 16 a b c d + 4 a b c )x + 2 a d
+
5     3       4 2 2 2      3 3 3       2 4 4
- 8 a b c d  + 12 a b c d  - 8 a b c d + 2 a b c
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(%e^(e/(c+d*x)^2)*(a+b*x)^3, x)
(214)
2       3   2
(- 8 a b d + 8 b c)e
+
3 3       2     2         2 2       3 3
(- 4 a d  + 12 a b c d  - 12 a b c d + 4 b c )e
*
+----+
|   e
d |- --
|   2
+---+     \|  d
\|%pi erf(--------)
d x + c
+
3 5 4        2 5 3     3 3       2   5  2
b d x  + 4 a b d x  + (b d e + 6 a b d )x
+
2 3      3   2        3 5           2   2      3 2
((8 a b d  - 6 b c d )e + 4 a d )x + (8 a b c d  - 7 b c d)e
+
3   4      2   2 3        2 3 2    3 4
4 a c d  - 6 a b c d  + 4 a b c d  - b c d
*
e
-------------------
2 2              2
d x  + 2 c d x + c
%e
+
3   2         2   3         2   2      3 2
(- b d e  + (- 6 a b d  + 12 a b c d  - 6 b c d)e)
*
e
Ei(-------------------)
2 2              2
d x  + 2 c d x + c
*
+----+
|   e
|- --
|   2
\|  d
/
+----+
5 |   e
4 d  |- --
|   2
\|  d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(%e^(e/(c+d*x)^2)*(a+b*x)^2, x)
(215)
+----+
|   e
d |- --
|   2
2 2         2 2                  2 2    +---+     \|  d
(- 2 b e  + (- 3 a d  + 6 a b c d - 3 b c )e)\|%pi erf(--------)
d x + c
+
2 4 3          4 2       2 2       2 4        2           2   3
b d x  + 3 a b d x  + (2 b d e + 3 a d )x + 2 b c d e + 3 a c d
+
2 2    2 3
- 3 a b c d  + b c d
*
e
-------------------
2 2              2
d x  + 2 c d x + c
%e
+
2      2                  e
(- 3 a b d  + 3 b c d)e Ei(-------------------)
2 2              2
d x  + 2 c d x + c
*
+----+
|   e
|- --
|   2
\|  d
/
+----+
4 |   e
3 d  |- --
|   2
\|  d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e/(c+d*x)^2)*(a+b*x), x)
(216)
+----+
|   e
d |- --
|   2
+---+     \|  d
(- 2 a d + 2 b c)e\|%pi erf(--------)
d x + c
+
e
-------------------
2 2              2
3 2        3           2      2    d x  + 2 c d x + c
(b d x  + 2 a d x + 2 a c d  - b c d)%e
+
e
- b d e Ei(-------------------)
2 2              2
d x  + 2 c d x + c
*
+----+
|   e
|- --
|   2
\|  d
/
+----+
3 |   e
2 d  |- --
|   2
\|  d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)^2), x)
+----+
|   e                           e
d |- --                  -------------------
|   2                   2 2              2 +----+
+---+     \|  d        2          d x  + 2 c d x + c  |   e
- e\|%pi erf(--------) + (d x + c d)%e                    |- --
d x + c                                     |   2
\|  d
(217)  ----------------------------------------------------------------
+----+
2 |   e
d  |- --
|   2
\|  d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)^2)/(a+b*x), x)
e
---------------------
2 2               2
x   %A d  + 2 %A c d + c
++  %e
(218)   |   ----------------------- d%A
++           %A b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e/(c+d*x)^2)/(a+b*x)^2, x)
e
---------------------
2 2               2
x   %A d  + 2 %A c d + c
++  %e
(219)   |   ----------------------- d%A
++      2 2               2
%A b  + 2 %A a b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)^2)/(a+b*x)^3, x)
e
---------------------
2 2               2
x        %A d  + 2 %A c d + c
++       %e
(220)   |   --------------------------------- d%A
++     3 3       2   2         2     3
%A b  + 3 %A a b  + 3 %A a b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(%e^(e/(c+d*x)^3)*(a+b*x)^3, x)
(221)
3 6 4        2 6 3      2   6 2       3 3       3 6
b d x  + 4 a b d x  + 6 a b d x  + (3 b d e + 4 a d )x
+
3   2       3   5      2   2 4        2 3 3    3 4 2
3 b c d e + 4 a c d  - 6 a b c d  + 4 a b c d  - b c d
*
e
------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
+
2 3      3   2                     e
(- 4 a b d  + 4 b c d )e Ei(------------------------------)
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
*
+----+2
|   e
|- --
3|   3
\|  d
+
2   3         2   2      3 2
(6 a b d  - 12 a b c d  + 6 b c d)e
*
+----+
1                  e                 |   e
Gamma(-,- ------------------------------)  |- --
3    3 3        2 2      2       3  3|   3
d x  + 3 c d x  + 3 c d x + c   \|  d
+
3 2       3 3       2     2         2 2       3 3
(3 b e  + (4 a d  - 12 a b c d  + 12 a b c d - 4 b c )e)
*
2                  e
Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
+----+2
6  |   e
4 d   |- --
3|   3
\|  d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)^3)*(a+b*x)^2, x)
(222)
2 5 3          5 2      2 5       2   4          2 3    2 3 2
(b d x  + 3 a b d x  + 3 a d x + 3 a c d  - 3 a b c d  + b c d )
*
e
------------------------------
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
%e
+
2 2                    e
- b d e Ei(------------------------------)
3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
*
+----+2
|   e
|- --
3|   3
\|  d
+
+----+
2      2            1                  e                 |   e
(3 a b d  - 3 b c d)e Gamma(-,- ------------------------------)  |- --
3    3 3        2 2      2       3  3|   3
d x  + 3 c d x  + 3 c d x + c   \|  d
+
2 2                  2 2         2                  e
(3 a d  - 6 a b c d + 3 b c )e Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
+----+2
5  |   e
3 d   |- --
3|   3
\|  d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e/(c+d*x)^3)*(a+b*x), x)
(223)
e
------------------------------
3 3        2 2      2       3
4 2        4           3      2 2   d x  + 3 c d x  + 3 c d x + c
(b d x  + 2 a d x + 2 a c d  - b c d )%e
*
+----+2
|   e
|- --
3|   3
\|  d
+
+----+
1                  e                 |   e
b d e Gamma(-,- ------------------------------)  |- --
3    3 3        2 2      2       3  3|   3
d x  + 3 c d x  + 3 c d x + c   \|  d
+
2                  e
(2 a d - 2 b c)e Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
+----+2
4  |   e
2 d   |- --
3|   3
\|  d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e/(c+d*x)^3), x)
(224)
e
------------------------------
3 3        2 2      2       3  +----+2
3       2   d x  + 3 c d x  + 3 c d x + c   |   e
(d x + c d )%e                                |- --
3|   3
\|  d
+
2                  e
e Gamma(-,- ------------------------------)
3    3 3        2 2      2       3
d x  + 3 c d x  + 3 c d x + c
/
+----+2
3  |   e
d   |- --
3|   3
\|  d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(%e^(e/(c+d*x)^3)/(a+b*x), x)
e
---------------------------------
3 3       2   2         2     3
x   %A d  + 3 %A c d  + 3 %A c d + c
++  %e
(225)   |   ----------------------------------- d%A
++                 %A b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)^3)/(a+b*x)^2, x)
e
---------------------------------
3 3       2   2         2     3
x   %A d  + 3 %A c d  + 3 %A c d + c
++  %e
(226)   |   ----------------------------------- d%A
++            2 2               2
%A b  + 2 %A a b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec