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 1 Editor: test1 Time: 2015/06/15 16:43:48 GMT+0 Note:

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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

-- Integration Problems Involving Exponentials

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

-- Integrands of the form (d+e x)^m F^(c (a+b x))
integrate(F^(c*(a+b*x))*(d+e*x)^m, x)
integrate(F^(c*(a+b*x))*(d+e*x)^4, x)
integrate(F^(c*(a+b*x))*(d+e*x)^3, x)
integrate(F^(c*(a+b*x))*(d+e*x)^2, x)
integrate(F^(c*(a+b*x))*(d+e*x), x)
integrate(F^(c*(a+b*x)), x)
integrate(F^(c*(a+b*x))/(d+e*x), x)
integrate(F^(c*(a+b*x))/(d+e*x)^2, x)
integrate(F^(c*(a+b*x))/(d+e*x)^3, x)
integrate(F^(c*(a+b*x))/(d+e*x)^4, x)
integrate(F^(c*(a+b*x))/(d+e*x)^5, x)
integrate(F^(c*(a+b*x))*(d^4+4*d^3*e*x+6*d^2*e^2*x^2+4*d*e^3*x^3+e^4*x^4), x)
integrate(F^(c*(a+b*x))*(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3), x)
integrate(F^(c*(a+b*x))*(d^2+2*d*e*x+e^2*x^2), x)
integrate(F^(c*(a+b*x))/(d^2+2*d*e*x+e^2*x^2), x)
integrate(F^(c*(a+b*x))/(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3), x)
integrate(F^(c*(a+b*x))/(d^4+4*d^3*e*x+6*d^2*e^2*x^2+4*d*e^3*x^3+e^4*x^4), x)
integrate(F^(c*(a+b*x))/(d^5+5*d^4*e*x+10*d^3*e^2*x^2+10*d^2*e^3*x^3+5*d*e^4*x^4+e^5*x^5), x)
integrate(F^(c*(a+b*x))*((d+e*x)^n)^m, x)
integrate(F^(c*(a+b*x))*(d^4+4*d^3*e*x+6*d^2*e^2*x^2+4*d*e^3*x^3+e^4*x^4)^m, x)
integrate(F^(c*(a+b*x))*(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3)^m, x)
integrate(F^(c*(a+b*x))*(d^2+2*d*e*x+e^2*x^2)^m, x)
integrate(F^(c*(a+b*x))*(d+e*x)^m, x)
integrate(F^(c*(a+b*x))/(d+e*x)^m, x)
integrate(F^(c*(a+b*x))/(d^2+2*d*e*x+e^2*x^2)^m, x)
integrate(F^(c*(a+b*x))/(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3)^m, x)
integrate(F^(2+5*x), x)
integrate(F^(a+b*x), x)
integrate(10^(2+5*x), x)

-- Integrands of the form (d+e x)^(m/2) F^(c (a+b x))
integrate(F^(a+b*x)*x^(7/2), x)
integrate(F^(a+b*x)*x^(5/2), x)
integrate(F^(a+b*x)*x^(3/2), x)
integrate(F^(a+b*x)*x^(1/2), x)
integrate(F^(a+b*x)/x^(1/2), x)
integrate(F^(a+b*x)/x^(3/2), x)
integrate(F^(a+b*x)/x^(5/2), x)
integrate(F^(a+b*x)/x^(7/2), x)
integrate(F^(a+b*x)/x^(9/2), x)
integrate(F^(c*(a+b*x))*(d+e*x)^(7/2), x)
integrate(F^(c*(a+b*x))*(d+e*x)^(5/2), x)
integrate(F^(c*(a+b*x))*(d+e*x)^(3/2), x)
integrate(F^(c*(a+b*x))*(d+e*x)^(1/2), x)
integrate(F^(c*(a+b*x))/(d+e*x)^(1/2), x)
integrate(F^(c*(a+b*x))/(d+e*x)^(3/2), x)
integrate(F^(c*(a+b*x))/(d+e*x)^(5/2), x)
integrate(F^(c*(a+b*x))/(d+e*x)^(7/2), x)
integrate(F^(c*(a+b*x))/(d+e*x)^(9/2), x)
integrate(x^(13/2)/%e^(b*x), x)

-- Integrands of the form Px F^(c (a+b x))
integrate(F^(c*(a+b*x))*(d+e*x), x)
integrate(F^(c*(a+b*x))*(d+e*x+f*x^2), x)
integrate(F^(c*(a+b*x))*(d+e*x+f*x^2+g*x^3), x)
integrate(F^(c*(a+b*x))*(d+e*x+f*x^2+g*x^3+h*x^4), x)

-- Integrands of the form x^m (e+f x)^n F^(a+b (c+d x))
integrate(%e^(-a-b*x)*x^m*(a+b*x)^3, x)
integrate(%e^(-a-b*x)*x^3*(a+b*x)^3, x)
integrate(%e^(-a-b*x)*x^2*(a+b*x)^3, x)
integrate(%e^(-a-b*x)*x*(a+b*x)^3, x)
integrate(%e^(-a-b*x)*(a+b*x)^3, x)
integrate(%e^(-a-b*x)*(a+b*x)^3/x, x)
integrate(%e^(-a-b*x)*(a+b*x)^3/x^2, x)
integrate(%e^(-a-b*x)*(a+b*x)^3/x^3, x)
integrate(%e^(-a-b*x)*(a+b*x)^3/x^4, x)
integrate(F^(a+b*(c+d*x))*x^m*(e+f*x)^2, x)
integrate(F^(a+b*(c+d*x))*x^3*(e+f*x)^2, x)
integrate(F^(a+b*(c+d*x))*x^2*(e+f*x)^2, x)
integrate(F^(a+b*(c+d*x))*x*(e+f*x)^2, x)
integrate(F^(a+b*(c+d*x))*(e+f*x)^2, x)
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x, x)
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^2, x)
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^3, x)
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^4, x)
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^5, x)

-- Integrands of the form (c+d x)^m (a+b x)^n F^(e (a+b x))
integrate(%e^(-a-b*x)*(a+b*x)^4*(c+d*x)^3, x)
integrate(%e^(-a-b*x)*(a+b*x)^4*(c+d*x)^2, x)
integrate(%e^(-a-b*x)*(a+b*x)^4*(c+d*x), x)
integrate(%e^(-a-b*x)*(a+b*x)^4, x)
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x), x)
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^2, x)
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^3, x)
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^4, x)
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^5, x)

-- Integrands of the form x^m F(c (a+b x)) Logintegrate(d x] (e+(f+g x) Log[d x])
integrate(F^(c*(a+b*x))*x^m*log(d*x)^n*(e+e*n+e*(1+m+b*c*x*log(F))*log(d*x)), x)
integrate(F^(c*(a+b*x))*x^2*log(d*x)^n*(e+e*n+e*(3+b*c*x*log(F))*log(d*x)), x)
integrate(F^(c*(a+b*x))*x*log(d*x)^n*(e+e*n+e*(2+b*c*x*log(F))*log(d*x)), x)
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+e*(1+b*c*x*log(F))*log(d*x)), x)
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+b*c*e*x*log(F)*log(d*x))/x, x)
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+e*(-1+b*c*x*log(F))*log(d*x))/x^2, x)
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+e*(-2+b*c*x*log(F))*log(d*x))/x^3, x)

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

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

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

-- n symbolic
integrate(f^(a+b*x^n)*x^m, x)
integrate(f^(a+b*x^n)*x^3, x)
integrate(f^(a+b*x^n)*x^2, x)
integrate(f^(a+b*x^n)*x, x)
integrate(f^(a+b*x^n), x)
integrate(f^(a+b*x^n)/x, x)
integrate(f^(a+b*x^n)/x^2, x)
integrate(f^(a+b*x^n)/x^3, x)
integrate(f^(a+b*x^n)/x^4, x)
integrate(f^(a+b*x^n)*x^(-1+3*n), x)
integrate(f^(a+b*x^n)*x^(-1+2*n), x)
integrate(f^(a+b*x^n)*x^(-1+n), x)
integrate(f^(a+b*x^n)/x, x)
integrate(f^(a+b*x^n)*x^(-1-n), x)
integrate(f^(a+b*x^n)*x^(-1-2*n), x)
integrate(f^(a+b*x^n)*x^(-1+5/2*n), x)
integrate(f^(a+b*x^n)*x^(-1+3/2*n), x)
integrate(f^(a+b*x^n)*x^(-1+1/2*n), x)
integrate(f^(a+b*x^n)*x^(-1-1/2*n), x)
integrate(f^(a+b*x^n)*x^(-1-3/2*n), x)
integrate(%e^((-0.1)*x)*x, 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
-- Integration Problems Involving Exponentials
-- Integrands of the form u F^(c (a+b x))
-- Integrands of the form (d+e x)^m F^(c (a+b x))
integrate(F^(c*(a+b*x))*(d+e*x)^m, x)
(1)
(- b c e x - b c d)log(F)
Gamma(m + 1,-------------------------)
e
*
b c log(F)
- e m log(- ----------) + (a c e - b c d)log(F)
e
-----------------------------------------------
e
%e
/
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.03 (EV) + 0.19 (OT) = 0.23 sec
integrate(F^(c*(a+b*x))*(d+e*x)^4, x)
(2)
4 4 4 4      4 4   3 3      4 4 2 2 2      4 4 3       4 4 4       4
(b c e x  + 4 b c d e x  + 6 b c d e x  + 4 b c d e x + b c d )log(F)
+
3 3 4 3       3 3   3 2       3 3 2 2       3 3 3        3
(- 4 b c e x  - 12 b c d e x  - 12 b c d e x - 4 b c d e)log(F)
+
2 2 4 2       2 2   3        2 2 2 2       2
(12 b c e x  + 24 b c d e x + 12 b c d e )log(F)
+
4              3              4
(- 24 b c e x - 24 b c d e )log(F) + 24 e
*
(b c x + a c)log(F)
%e
/
5 5      5
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x)^3, x)
(3)
3 3 3 3      3 3   2 2      3 3 2       3 3 3       3
(b c e x  + 3 b c d e x  + 3 b c d e x + b c d )log(F)
+
2 2 3 2      2 2   2       2 2 2        2
(- 3 b c e x  - 6 b c d e x - 3 b c d e)log(F)
+
3             2             3
(6 b c e x + 6 b c d e )log(F) - 6 e
*
(b c x + a c)log(F)
%e
/
4 4      4
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*(d+e*x)^2, x)
(4)
2 2 2 2      2 2         2 2 2       2
(b c e x  + 2 b c d e x + b c d )log(F)
+
2                          2
(- 2 b c e x - 2 b c d e)log(F) + 2 e
*
(b c x + a c)log(F)
%e
/
3 3      3
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x), x)
(b c x + a c)log(F)
((b c e x + b c d)log(F) - e)%e
(5)  --------------------------------------------------
2 2      2
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x)), x)
(b c x + a c)log(F)
%e
(6)  ---------------------
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d+e*x), x)
(a c e - b c d)log(F)
---------------------
(b c e x + b c d)log(F)             e
Ei(-----------------------)%e
e
(7)  --------------------------------------------------
e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^2, x)
(8)
(b c x + a c)log(F)
- e %e
+
(a c e - b c d)log(F)
---------------------
(b c e x + b c d)log(F)             e
(b c e x + b c d)log(F)Ei(-----------------------)%e
e
/
3       2
e x + d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d+e*x)^3, x)
(9)
2                      2   (b c x + a c)log(F)
((- b c e x - b c d e)log(F) - e )%e
+
2 2 2 2      2 2         2 2 2       2   (b c e x + b c d)log(F)
(b c e x  + 2 b c d e x + b c d )log(F) Ei(-----------------------)
e
*
(a c e - b c d)log(F)
---------------------
e
%e
/
5 2        4       2 3
2 e x  + 4 d e x + 2 d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d+e*x)^4, x)
(10)
2 2 3 2      2 2   2     2 2 2        2
(- b c e x  - 2 b c d e x - b c d e)log(F)
+
3           2             3
(- b c e x - b c d e )log(F) - 2 e
*
(b c x + a c)log(F)
%e
+
3 3 3 3      3 3   2 2      3 3 2       3 3 3       3
(b c e x  + 3 b c d e x  + 3 b c d e x + b c d )log(F)
*
(a c e - b c d)log(F)
---------------------
(b c e x + b c d)log(F)             e
Ei(-----------------------)%e
e
/
7 3         6 2       2 5       3 4
6 e x  + 18 d e x  + 18 d e x + 6 d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^5, x)
(11)
3 3 4 3      3 3   3 2      3 3 2 2     3 3 3        3
(- b c e x  - 3 b c d e x  - 3 b c d e x - b c d e)log(F)
+
2 2 4 2      2 2   3     2 2 2 2       2
(- b c e x  - 2 b c d e x - b c d e )log(F)
+
4             3             4
(- 2 b c e x - 2 b c d e )log(F) - 6 e
*
(b c x + a c)log(F)
%e
+
4 4 4 4      4 4   3 3      4 4 2 2 2      4 4 3       4 4 4       4
(b c e x  + 4 b c d e x  + 6 b c d e x  + 4 b c d e x + b c d )log(F)
*
(a c e - b c d)log(F)
---------------------
(b c e x + b c d)log(F)             e
Ei(-----------------------)%e
e
/
9 4         8 3        2 7 2       3 6        4 5
24 e x  + 96 d e x  + 144 d e x  + 96 d e x + 24 d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d^4+4*d^3*e*x+6*d^2*e^2*x^2+4*d*e^3*x^3+e^4*x^4), x)
(12)
4 4 4 4      4 4   3 3      4 4 2 2 2      4 4 3       4 4 4       4
(b c e x  + 4 b c d e x  + 6 b c d e x  + 4 b c d e x + b c d )log(F)
+
3 3 4 3       3 3   3 2       3 3 2 2       3 3 3        3
(- 4 b c e x  - 12 b c d e x  - 12 b c d e x - 4 b c d e)log(F)
+
2 2 4 2       2 2   3        2 2 2 2       2
(12 b c e x  + 24 b c d e x + 12 b c d e )log(F)
+
4              3              4
(- 24 b c e x - 24 b c d e )log(F) + 24 e
*
(b c x + a c)log(F)
%e
/
5 5      5
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3), x)
(13)
3 3 3 3      3 3   2 2      3 3 2       3 3 3       3
(b c e x  + 3 b c d e x  + 3 b c d e x + b c d )log(F)
+
2 2 3 2      2 2   2       2 2 2        2
(- 3 b c e x  - 6 b c d e x - 3 b c d e)log(F)
+
3             2             3
(6 b c e x + 6 b c d e )log(F) - 6 e
*
(b c x + a c)log(F)
%e
/
4 4      4
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*(d^2+2*d*e*x+e^2*x^2), x)
(14)
2 2 2 2      2 2         2 2 2       2
(b c e x  + 2 b c d e x + b c d )log(F)
+
2                          2
(- 2 b c e x - 2 b c d e)log(F) + 2 e
*
(b c x + a c)log(F)
%e
/
3 3      3
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d^2+2*d*e*x+e^2*x^2), x)
(15)
(b c x + a c)log(F)
- e %e
+
(a c e - b c d)log(F)
---------------------
(b c e x + b c d)log(F)             e
(b c e x + b c d)log(F)Ei(-----------------------)%e
e
/
3       2
e x + d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3), x)
(16)
2                      2   (b c x + a c)log(F)
((- b c e x - b c d e)log(F) - e )%e
+
2 2 2 2      2 2         2 2 2       2   (b c e x + b c d)log(F)
(b c e x  + 2 b c d e x + b c d )log(F) Ei(-----------------------)
e
*
(a c e - b c d)log(F)
---------------------
e
%e
/
5 2        4       2 3
2 e x  + 4 d e x + 2 d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d^4+4*d^3*e*x+6*d^2*e^2*x^2+4*d*e^3*x^3+e^4*x^4), x)
(17)
2 2 3 2      2 2   2     2 2 2        2
(- b c e x  - 2 b c d e x - b c d e)log(F)
+
3           2             3
(- b c e x - b c d e )log(F) - 2 e
*
(b c x + a c)log(F)
%e
+
3 3 3 3      3 3   2 2      3 3 2       3 3 3       3
(b c e x  + 3 b c d e x  + 3 b c d e x + b c d )log(F)
*
(a c e - b c d)log(F)
---------------------
(b c e x + b c d)log(F)             e
Ei(-----------------------)%e
e
/
7 3         6 2       2 5       3 4
6 e x  + 18 d e x  + 18 d e x + 6 d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d^5+5*d^4*e*x+10*d^3*e^2*x^2+10*d^2*e^3*x^3+5*d*e^4*x^4+e^5*x^5), x)
(18)
3 3 4 3      3 3   3 2      3 3 2 2     3 3 3        3
(- b c e x  - 3 b c d e x  - 3 b c d e x - b c d e)log(F)
+
2 2 4 2      2 2   3     2 2 2 2       2
(- b c e x  - 2 b c d e x - b c d e )log(F)
+
4             3             4
(- 2 b c e x - 2 b c d e )log(F) - 6 e
*
(b c x + a c)log(F)
%e
+
4 4 4 4      4 4   3 3      4 4 2 2 2      4 4 3       4 4 4       4
(b c e x  + 4 b c d e x  + 6 b c d e x  + 4 b c d e x + b c d )log(F)
*
(a c e - b c d)log(F)
---------------------
(b c e x + b c d)log(F)             e
Ei(-----------------------)%e
e
/
9 4         8 3        2 7 2       3 6        4 5
24 e x  + 96 d e x  + 144 d e x  + 96 d e x + 24 d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*((d+e*x)^n)^m, x)
(19)
(- b c e x - b c d)log(F)
Gamma(m n + 1,-------------------------)
e
*
b c log(F)
- e m n log(- ----------) + (a c e - b c d)log(F)
e
-------------------------------------------------
e
%e
/
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d^4+4*d^3*e*x+6*d^2*e^2*x^2+4*d*e^3*x^3+e^4*x^4)^m, x)
x
++   (%A b + a)c   4 4       3   3       2 2 2         3     4 m
(20)   |   F           (%A e  + 4 %A d e  + 6 %A d e  + 4 %A d e + d ) d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3)^m, x)
x
++   (%A b + a)c   3 3       2   2         2     3 m
(21)   |   F           (%A e  + 3 %A d e  + 3 %A d e + d ) d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*(d^2+2*d*e*x+e^2*x^2)^m, x)
x
++   (%A b + a)c   2 2               2 m
(22)   |   F           (%A e  + 2 %A d e + d ) d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x)^m, x)
(23)
(- b c e x - b c d)log(F)
Gamma(m + 1,-------------------------)
e
*
b c log(F)
- e m log(- ----------) + (a c e - b c d)log(F)
e
-----------------------------------------------
e
%e
/
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d+e*x)^m, x)
(24)
(- b c e x - b c d)log(F)
Gamma(- m + 1,-------------------------)
e
*
b c log(F)
e m log(- ----------) + (a c e - b c d)log(F)
e
---------------------------------------------
e
%e
/
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d^2+2*d*e*x+e^2*x^2)^m, x)
x        (%A b + a)c
++        F
(25)   |   ------------------------ d%A
++      2 2               2 m
(%A e  + 2 %A d e + d )
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3)^m, x)
x              (%A b + a)c
++              F
(26)   |   ------------------------------------ d%A
++      3 3       2   2         2     3 m
(%A e  + 3 %A d e  + 3 %A d e + d )
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(F^(2+5*x), x)
(5 x + 2)log(F)
%e
(27)  -----------------
5 log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*x), x)
(b x + a)log(F)
%e
(28)  -----------------
b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(10^(2+5*x), x)
(5 x + 2)log(10)
%e
(29)  ------------------
5 log(10)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
-- Integrands of the form (d+e x)^(m/2) F^(c (a+b x))
integrate(F^(a+b*x)*x^(7/2), x)
(30)
+---+  a log(F)     +-+ +----------+
105 \|%pi %e        erf(\|x \|- b log(F) )
+
3 3      3       2 2      2                         +-+
(16 b x log(F)  - 56 b x log(F)  + 140 b x log(F) - 210)\|x
*
(b x + a)log(F) +----------+
%e               \|- b log(F)
/
4      4 +----------+
16 b log(F) \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*x)*x^(5/2), x)
(31)
+---+  a log(F)     +-+ +----------+
- 15 \|%pi %e        erf(\|x \|- b log(F) )
+
2 2      2                       +-+  (b x + a)log(F) +----------+
(8 b x log(F)  - 20 b x log(F) + 30)\|x %e               \|- b log(F)
/
3      3 +----------+
8 b log(F) \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*x)*x^(3/2), x)
(32)
+---+  a log(F)     +-+ +----------+
3 \|%pi %e        erf(\|x \|- b log(F) )
+
+-+  (b x + a)log(F) +----------+
(4 b x log(F) - 6)\|x %e               \|- b log(F)
/
2      2 +----------+
4 b log(F) \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*x)*x^(1/2), x)
(33)
+---+  a log(F)     +-+ +----------+
- \|%pi %e        erf(\|x \|- b log(F) )
+
+-+  (b x + a)log(F) +----------+
2 \|x %e               \|- b log(F)
/
+----------+
2 b log(F)\|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*x)/x^(1/2), x)
+---+  a log(F)     +-+ +----------+
\|%pi %e        erf(\|x \|- b log(F) )
(34)  --------------------------------------
+----------+
\|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*x)/x^(3/2), x)
(35)
+---+ +-+  a log(F)     +-+ +----------+
2 b log(F)\|%pi \|x %e        erf(\|x \|- b log(F) )
+
(b x + a)log(F) +----------+
- 2 %e               \|- b log(F)
/
+-+ +----------+
\|x \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*x)/x^(5/2), x)
(36)
2        2 +---+ +-+  a log(F)     +-+ +----------+
4 b x log(F) \|%pi \|x %e        erf(\|x \|- b log(F) )
+
(b x + a)log(F) +----------+
(- 4 b x log(F) - 2)%e               \|- b log(F)
/
+-+ +----------+
3 x\|x \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*x)/x^(7/2), x)
(37)
3 2      3 +---+ +-+  a log(F)     +-+ +----------+
8 b x log(F) \|%pi \|x %e        erf(\|x \|- b log(F) )
+
2 2      2                      (b x + a)log(F) +----------+
(- 8 b x log(F)  - 4 b x log(F) - 6)%e               \|- b log(F)
/
2 +-+ +----------+
15 x \|x \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*x)/x^(9/2), x)
(38)
4 3      4 +---+ +-+  a log(F)     +-+ +----------+
16 b x log(F) \|%pi \|x %e        erf(\|x \|- b log(F) )
+
3 3      3      2 2      2
(- 16 b x log(F)  - 8 b x log(F)  - 12 b x log(F) - 30)
*
(b x + a)log(F) +----------+
%e               \|- b log(F)
/
3 +-+ +----------+
105 x \|x \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x)^(7/2), x)
(39)
(a c e - b c d)log(F)
---------------------               +------------+
3 +---+            e               +-------+ |  b c log(F)
105 e \|%pi %e                     erf(\|e x + d  |- ---------- )
\|       e
+
3 3 3 3       3 3   2 2       3 3 2          3 3 3       3
(16 b c e x  + 48 b c d e x  + 48 b c d e x + 16 b c d )log(F)
+
2 2 3 2        2 2   2        2 2 2        2
(- 56 b c e x  - 112 b c d e x - 56 b c d e)log(F)
+
3               2               3
(140 b c e x + 140 b c d e )log(F) - 210 e
*
+------------+
+-------+  (b c x + a c)log(F) |  b c log(F)
\|e x + d %e                    |- ----------
\|       e
/
+------------+
4 4      4 |  b c log(F)
16 b c log(F)  |- ----------
\|       e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*(d+e*x)^(5/2), x)
(40)
(a c e - b c d)log(F)
---------------------               +------------+
2 +---+            e               +-------+ |  b c log(F)
- 15 e \|%pi %e                     erf(\|e x + d  |- ---------- )
\|       e
+
2 2 2 2       2 2           2 2 2       2
(8 b c e x  + 16 b c d e x + 8 b c d )log(F)
+
2                            2
(- 20 b c e x - 20 b c d e)log(F) + 30 e
*
+------------+
+-------+  (b c x + a c)log(F) |  b c log(F)
\|e x + d %e                    |- ----------
\|       e
/
+------------+
3 3      3 |  b c log(F)
8 b c log(F)  |- ----------
\|       e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x)^(3/2), x)
(41)
(a c e - b c d)log(F)
---------------------               +------------+
+---+            e               +-------+ |  b c log(F)
3 e\|%pi %e                     erf(\|e x + d  |- ---------- )
\|       e
+
+-------+  (b c x + a c)log(F)
((4 b c e x + 4 b c d)log(F) - 6 e)\|e x + d %e
*
+------------+
|  b c log(F)
|- ----------
\|       e
/
+------------+
2 2      2 |  b c log(F)
4 b c log(F)  |- ----------
\|       e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*(d+e*x)^(1/2), x)
(42)
(a c e - b c d)log(F)
---------------------               +------------+
+---+            e               +-------+ |  b c log(F)
- \|%pi %e                     erf(\|e x + d  |- ---------- )
\|       e
+
+------------+
+-------+  (b c x + a c)log(F) |  b c log(F)
2 \|e x + d %e                    |- ----------
\|       e
/
+------------+
|  b c log(F)
2 b c log(F) |- ----------
\|       e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^(1/2), x)
(a c e - b c d)log(F)
---------------------               +------------+
+---+            e               +-------+ |  b c log(F)
\|%pi %e                     erf(\|e x + d  |- ---------- )
\|       e
(43)  -----------------------------------------------------------
+------------+
|  b c log(F)
e |- ----------
\|       e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d+e*x)^(3/2), x)
(44)
(a c e - b c d)log(F)
---------------------
+---+ +-------+            e
2 b c log(F)\|%pi \|e x + d %e
*
+------------+
+-------+ |  b c log(F)
erf(\|e x + d  |- ---------- )
\|       e
+
+------------+
(b c x + a c)log(F) |  b c log(F)
- 2 e %e                    |- ----------
\|       e
/
+------------+
2 +-------+ |  b c log(F)
e \|e x + d  |- ----------
\|       e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^(5/2), x)
(45)
(a c e - b c d)log(F)
---------------------
2 2         2 2        2 +---+ +-------+            e
(4 b c e x + 4 b c d)log(F) \|%pi \|e x + d %e
*
+------------+
+-------+ |  b c log(F)
erf(\|e x + d  |- ---------- )
\|       e
+
2                          2   (b c x + a c)log(F)
((- 4 b c e x - 4 b c d e)log(F) - 2 e )%e
*
+------------+
|  b c log(F)
|- ----------
\|       e
/
+------------+
4         3  +-------+ |  b c log(F)
(3 e x + 3 d e )\|e x + d  |- ----------
\|       e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^(7/2), x)
(46)
3 3 2 2       3 3           3 3 2       3 +---+ +-------+
(8 b c e x  + 16 b c d e x + 8 b c d )log(F) \|%pi \|e x + d
*
(a c e - b c d)log(F)
---------------------               +------------+
e               +-------+ |  b c log(F)
%e                     erf(\|e x + d  |- ---------- )
\|       e
+
2 2 3 2       2 2   2       2 2 2        2
(- 8 b c e x  - 16 b c d e x - 8 b c d e)log(F)
+
3             2             3
(- 4 b c e x - 4 b c d e )log(F) - 6 e
*
+------------+
(b c x + a c)log(F) |  b c log(F)
%e                    |- ----------
\|       e
/
+------------+
6 2         5        2 4  +-------+ |  b c log(F)
(15 e x  + 30 d e x + 15 d e )\|e x + d  |- ----------
\|       e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d+e*x)^(9/2), x)
(47)
4 4 3 3       4 4   2 2       4 4 2          4 4 3       4 +---+
(16 b c e x  + 48 b c d e x  + 48 b c d e x + 16 b c d )log(F) \|%pi
*
(a c e - b c d)log(F)
---------------------               +------------+
+-------+            e               +-------+ |  b c log(F)
\|e x + d %e                     erf(\|e x + d  |- ---------- )
\|       e
+
3 3 4 3       3 3   3 2       3 3 2 2        3 3 3        3
(- 16 b c e x  - 48 b c d e x  - 48 b c d e x - 16 b c d e)log(F)
+
2 2 4 2       2 2   3       2 2 2 2       2
(- 8 b c e x  - 16 b c d e x - 8 b c d e )log(F)
+
4              3              4
(- 12 b c e x - 12 b c d e )log(F) - 30 e
*
+------------+
(b c x + a c)log(F) |  b c log(F)
%e                    |- ----------
\|       e
/
+------------+
8 3          7 2        2 6         3 5  +-------+ |  b c log(F)
(105 e x  + 315 d e x  + 315 d e x + 105 d e )\|e x + d  |- ----------
\|       e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(x^(13/2)/%e^(b*x), x)
(48)
b x +---+     +-+ +-+
135135 %e   \|%pi erf(\|b \|x )
+
6 6        5 5         4 4          3 3          2 2
- 128 b x  - 832 b x  - 4576 b x  - 20592 b x  - 72072 b x
+
- 180180 b x - 270270
*
+-+ +-+
\|b \|x
/
7  b x +-+
128 b %e   \|b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
-- Integrands of the form Px F^(c (a+b x))
integrate(F^(c*(a+b*x))*(d+e*x), x)
(b c x + a c)log(F)
((b c e x + b c d)log(F) - e)%e
(49)  --------------------------------------------------
2 2      2
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*(d+e*x+f*x^2), x)
(50)
2 2   2    2 2       2 2        2
((b c f x  + b c e x + b c d)log(F)  + (- 2 b c f x - b c e)log(F) + 2 f)
*
(b c x + a c)log(F)
%e
/
3 3      3
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*(d+e*x+f*x^2+g*x^3), x)
(51)
3 3   3    3 3   2    3 3       3 3        3
(b c g x  + b c f x  + b c e x + b c d)log(F)
+
2 2   2      2 2       2 2        2
(- 3 b c g x  - 2 b c f x - b c e)log(F)  + (6 b c g x + 2 b c f)log(F)
+
- 6 g
*
(b c x + a c)log(F)
%e
/
4 4      4
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x+f*x^2+g*x^3+h*x^4), x)
(52)
4 4   4    4 4   3    4 4   2    4 4       4 4        4
(b c h x  + b c g x  + b c f x  + b c e x + b c d)log(F)
+
3 3   3      3 3   2      3 3       3 3        3
(- 4 b c h x  - 3 b c g x  - 2 b c f x - b c e)log(F)
+
2 2   2      2 2         2 2        2
(12 b c h x  + 6 b c g x + 2 b c f)log(F)
+
(- 24 b c h x - 6 b c g)log(F) + 24 h
*
(b c x + a c)log(F)
%e
/
5 5      5
b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
-- Integrands of the form x^m (e+f x)^n F^(a+b (c+d x))
integrate(%e^(-a-b*x)*x^m*(a+b*x)^3, x)
(53)
3 3       2                2  2
- b x  + (- b m + (- 3 a - 3)b )x
+
2                          2
(- b m  + (- 3 a - 5)b m + (- 3 a  - 6 a - 6)b)x
*
- b x - a  m log(x)
%e         %e
+
3               2         2                 3      2
(- m  + (- 3 a - 6)m  + (- 3 a  - 9 a - 11)m - a  - 3 a  - 6 a - 6)
*
- m log(b) - a
Gamma(m + 1,b x)%e
/
b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*x^3*(a+b*x)^3, x)
(54)
6 6               5 5         2              4 4
- b x  + (- 3 a - 6)b x  + (- 3 a  - 15 a - 30)b x
+
3       2               3 3         3       2                2 2
(- a  - 12 a  - 60 a - 120)b x  + (- 3 a  - 36 a  - 180 a - 360)b x
+
3       2                        3       2
(- 6 a  - 72 a  - 360 a - 720)b x - 6 a  - 72 a  - 360 a - 720
*
- b x - a
%e
/
4
b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*x^2*(a+b*x)^3, x)
(55)
5 5               4 4         2              3 3
- b x  + (- 3 a - 5)b x  + (- 3 a  - 12 a - 20)b x
+
3      2              2 2         3       2                       3
(- a  - 9 a  - 36 a - 60)b x  + (- 2 a  - 18 a  - 72 a - 120)b x - 2 a
+
2
- 18 a  - 72 a - 120
*
- b x - a
%e
/
3
b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*x*(a+b*x)^3, x)
(56)
4 4               3 3         2             2 2
- b x  + (- 3 a - 4)b x  + (- 3 a  - 9 a - 12)b x
+
3      2                    3      2
(- a  - 6 a  - 18 a - 24)b x - a  - 6 a  - 18 a - 24
*
- b x - a
%e
/
2
b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*(a+b*x)^3, x)
(57)
3 3               2 2         2                  3      2
(- b x  + (- 3 a - 3)b x  + (- 3 a  - 6 a - 6)b x - a  - 3 a  - 6 a - 6)
*
- b x - a
%e
/
b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^3/x, x)
(58)
3           - a       2 2                       2             - b x - a
a Ei(- b x)%e    + (- b x  + (- 3 a - 2)b x - 3 a  - 3 a - 2)%e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*(a+b*x)^3/x^2, x)
(59)
3      2                - a       2 2                     3   - b x - a
(- a  + 3 a )b x Ei(- b x)%e    + (- b x  + (- 3 a - 1)b x - a )%e
---------------------------------------------------------------------------
x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^3/x^3, x)
(60)
3      2        2 2           - a
(a  - 6 a  + 6 a)b x Ei(- b x)%e
+
2 2     3      2        3   - b x - a
(- 2 b x  + (a  - 6 a )b x - a )%e
/
2
2 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^3/x^4, x)
(61)
3      2             3 3           - a
(- a  + 9 a  - 18 a + 6)b x Ei(- b x)%e
+
3      2         2 2     3      2          3   - b x - a
((- a  + 9 a  - 18 a)b x  + (a  - 9 a )b x - 2 a )%e
/
3
6 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x))*x^m*(e+f*x)^2, x)
(62)
2 2 2      2                                        2 2      2
b d e log(F)  + (- 2 b d e f m - 2 b d e f)log(F) + f m  + 3 f m
+
2
2 f
*
- m log(- b d log(F)) + (b c + a)log(F)
Gamma(m + 1,- b d x log(F))%e
+
2 2 2 2      2 2            2           2           2
((b d f x  + 2 b d e f x)log(F)  + (- b d f m - 2 b d f )x log(F))
*
(b d x + b c + a)log(F)  m log(x)
%e                       %e
/
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))*x^3*(e+f*x)^2, x)
(63)
5 5 2 5      5 5     4    5 5 2 3       5
(b d f x  + 2 b d e f x  + b d e x )log(F)
+
4 4 2 4      4 4     3      4 4 2 2       4
(- 5 b d f x  - 8 b d e f x  - 3 b d e x )log(F)
+
3 3 2 3       3 3     2      3 3 2        3
(20 b d f x  + 24 b d e f x  + 6 b d e x)log(F)
+
2 2 2 2       2 2           2 2 2       2
(- 60 b d f x  - 48 b d e f x - 6 b d e )log(F)
+
2                             2
(120 b d f x + 48 b d e f)log(F) - 120 f
*
(b d x + b c + a)log(F)
%e
/
6 6      6
b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.05 (EV) = 0.05 sec
integrate(F^(a+b*(c+d*x))*x^2*(e+f*x)^2, x)
(64)
4 4 2 4      4 4     3    4 4 2 2       4
(b d f x  + 2 b d e f x  + b d e x )log(F)
+
3 3 2 3      3 3     2      3 3 2        3
(- 4 b d f x  - 6 b d e f x  - 2 b d e x)log(F)
+
2 2 2 2       2 2           2 2 2       2
(12 b d f x  + 12 b d e f x + 2 b d e )log(F)
+
2                            2
(- 24 b d f x - 12 b d e f)log(F) + 24 f
*
(b d x + b c + a)log(F)
%e
/
5 5      5
b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x))*x*(e+f*x)^2, x)
(65)
3 3 2 3      3 3     2    3 3 2        3
(b d f x  + 2 b d e f x  + b d e x)log(F)
+
2 2 2 2      2 2         2 2 2       2
(- 3 b d f x  - 4 b d e f x - b d e )log(F)
+
2                          2
(6 b d f x + 4 b d e f)log(F) - 6 f
*
(b d x + b c + a)log(F)
%e
/
4 4      4
b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x))*(e+f*x)^2, x)
(66)
2 2 2 2      2 2         2 2 2       2
(b d f x  + 2 b d e f x + b d e )log(F)
+
2                          2
(- 2 b d f x - 2 b d e f)log(F) + 2 f
*
(b 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))*(e+f*x)^2/x, x)
(67)
2                        2   (b d x + b c + a)log(F)
((b d f x + 2 b d e f)log(F) - f )%e
+
2 2 2      2                  (b c + a)log(F)
b d e log(F) Ei(b d x log(F))%e
/
2 2      2
b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^2, x)
(68)
2          2    (b d x + b c + a)log(F)
(- b d e log(F) + f x)%e
+
2 2 2        2                                        (b c + a)log(F)
(b d e x log(F)  + 2 b d e f x log(F))Ei(b d x log(F))%e
/
b d x log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^3, x)
(69)
2                      2   (b d x + b c + a)log(F)
(- b d e x log(F) - 4 e f x - e )%e
+
2 2 2 2      2              2            2 2
(b d e x log(F)  + 4 b d e f x log(F) + 2 f x )Ei(b d x log(F))
*
(b c + a)log(F)
%e
/
2
2 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^4, x)
(70)
2 2 2 2      2                 2        2              2 2
- b d e x log(F)  + (- 6 b d e f x  - b d e x)log(F) - 6 f x
+
2
- 6 e f x - 2 e
*
(b d x + b c + a)log(F)
%e
+
3 3 2 3      3      2 2     3      2          2 3
(b d e x log(F)  + 6 b d e f x log(F)  + 6 b d f x log(F))
*
(b c + a)log(F)
Ei(b d x log(F))%e
/
3
6 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^5, x)
(71)
3 3 2 3      3         2 2     3    2 2 2 2       2
- b d e x log(F)  + (- 8 b d e f x  - b d e x )log(F)
+
2 3              2          2               2 2
(- 12 b d f x  - 8 b d e f x  - 2 b d e x)log(F) - 12 f x  - 16 e f x
+
2
- 6 e
*
(b d x + b c + a)log(F)
%e
+
4 4 2 4      4      3 3     4      3       2 2 2 4      2
(b d e x log(F)  + 8 b d e f x log(F)  + 12 b d f x log(F) )
*
(b c + a)log(F)
Ei(b d x log(F))%e
/
4
24 x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
-- Integrands of the form (c+d x)^m (a+b x)^n F^(e (a+b x))
integrate(%e^(-a-b*x)*(a+b*x)^4*(c+d*x)^3, x)
(72)
7 3 7                6 3      7   2  6
- b d x  + ((- 4 a - 7)b d  - 3 b c d )x
+
2              5 3                 6   2      7 2   5
((- 6 a  - 24 a - 42)b d  + (- 12 a - 18)b c d  - 3 b c d)x
+
3       2                4 3          2              5   2
(- 4 a  - 30 a  - 120 a - 210)b d  + (- 18 a  - 60 a - 90)b c d
+
6 2     7 3
(- 12 a - 15)b c d - b c
*
4
x
+
4       3        2                3 3
(- a  - 16 a  - 120 a  - 480 a - 840)b d
+
3       2                4   2          2              5 2
(- 12 a  - 72 a  - 240 a - 360)b c d  + (- 18 a  - 48 a - 60)b c d
+
6 3
(- 4 a - 4)b c
*
3
x
+
4       3        2                  2 3
(- 3 a  - 48 a  - 360 a  - 1440 a - 2520)b d
+
4       3        2                 3   2
(- 3 a  - 36 a  - 216 a  - 720 a - 1080)b c d
+
3       2                4 2          2              5 3
(- 12 a  - 54 a  - 144 a - 180)b c d + (- 6 a  - 12 a - 12)b c
*
2
x
+
4       3        2                    3
(- 6 a  - 96 a  - 720 a  - 2880 a - 5040)b d
+
4       3        2                  2   2
(- 6 a  - 72 a  - 432 a  - 1440 a - 2160)b c d
+
4       3        2                3 2
(- 3 a  - 24 a  - 108 a  - 288 a - 360)b c d
+
3       2              4 3
(- 4 a  - 12 a  - 24 a - 24)b c
*
x
+
4       3        2                  3
(- 6 a  - 96 a  - 720 a  - 2880 a - 5040)d
+
4       3        2                      2
(- 6 a  - 72 a  - 432 a  - 1440 a - 2160)b c d
+
4       3        2                2 2
(- 3 a  - 24 a  - 108 a  - 288 a - 360)b c d
+
4      3       2              3 3
(- a  - 4 a  - 12 a  - 24 a - 24)b c
*
- b x - a
%e
/
4
b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^4*(c+d*x)^2, x)
(73)
6 2 6                5 2      6     5
- b d x  + ((- 4 a - 6)b d  - 2 b c d)x
+
2              4 2                5       6 2  4
((- 6 a  - 20 a - 30)b d  + (- 8 a - 10)b c d - b c )x
+
3       2               3 2          2              4
(- 4 a  - 24 a  - 80 a - 120)b d  + (- 12 a  - 32 a - 40)b c d
+
5 2
(- 4 a - 4)b c
*
3
x
+
4       3       2                2 2
(- a  - 12 a  - 72 a  - 240 a - 360)b d
+
3       2               3            2              4 2
(- 8 a  - 36 a  - 96 a - 120)b c d + (- 6 a  - 12 a - 12)b c
*
2
x
+
4       3        2                  2
(- 2 a  - 24 a  - 144 a  - 480 a - 720)b d
+
4       3       2                2
(- 2 a  - 16 a  - 72 a  - 192 a - 240)b c d
+
3       2              3 2
(- 4 a  - 12 a  - 24 a - 24)b c
*
x
+
4       3        2                2
(- 2 a  - 24 a  - 144 a  - 480 a - 720)d
+
4       3       2
(- 2 a  - 16 a  - 72 a  - 192 a - 240)b c d
+
4      3       2              2 2
(- a  - 4 a  - 12 a  - 24 a - 24)b c
*
- b x - a
%e
/
3
b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*(a+b*x)^4*(c+d*x), x)
(74)
5   5                4     5   4
- b d x  + ((- 4 a - 5)b d - b c)x
+
2              3                4   3
((- 6 a  - 16 a - 20)b d + (- 4 a - 4)b c)x
+
3       2              2          2              3   2
((- 4 a  - 18 a  - 48 a - 60)b d + (- 6 a  - 12 a - 12)b c)x
+
4      3       2
(- a  - 8 a  - 36 a  - 96 a - 120)b d
+
3       2              2
(- 4 a  - 12 a  - 24 a - 24)b c
*
x
+
4      3       2
(- a  - 8 a  - 36 a  - 96 a - 120)d
+
4      3       2
(- a  - 4 a  - 12 a  - 24 a - 24)b c
*
- b x - a
%e
/
2
b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*(a+b*x)^4, x)
(75)
4 4               3 3         2              2 2
- b x  + (- 4 a - 4)b x  + (- 6 a  - 12 a - 12)b x
+
3       2                    4      3       2
(- 4 a  - 12 a  - 24 a - 24)b x - a  - 4 a  - 12 a  - 24 a - 24
*
- b x - a
%e
/
b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x), x)
(76)
4 4      3     3      2 2 2 2        3 3     4 4    - b d x - b c
(a d  - 4 a b c d  + 6 a b c d  - 4 a b c d + b c )Ei(-------------)
d
*
- a d + b c
-----------
d
%e
+
3 4 3                2 4    3   3  2
- b d x  + ((- 4 a - 3)b d  + b c d )x
+
2              4             2   3    3 2 2
((- 6 a  - 8 a - 6)b d  + (4 a + 2)b c d  - b c d )x
+
3      2            4       2                3
(- 4 a  - 6 a  - 8 a - 6)d  + (6 a  + 4 a + 2)b c d
+
2 2 2    3 3
(- 4 a - 1)b c d  + b c d
*
- b x - a
%e
/
5
d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^2, x)
(77)
4      3    5       3       2  2   4         2         3 2 3
(- a  + 4 a )b d  + (4 a  - 12 a )b c d  + (- 6 a  + 12 a)b c d
+
4 3 2    5 4
(4 a - 4)b c d  - b c d
*
x
+
4      3      4       3       2  2 2 3         2         3 3 2
(- a  + 4 a )b c d  + (4 a  - 12 a )b c d  + (- 6 a  + 12 a)b c d
+
4 4     5 5
(4 a - 4)b c d - b c
*
- a d + b c
-----------
- b d x - b c        d
Ei(-------------)%e
d
+
3 5 3                2 5    3   4  2
- b d x  + ((- 4 a - 2)b d  + b c d )x
+
2              5        2   4    3 2 3      4 5
((- 6 a  - 4 a - 2)b d  + 4 a b c d  - b c d )x - a d
+
3      2                4         2            2 2 3
(4 a  - 6 a  - 4 a - 2)b c d  + (- 6 a  + 8 a + 2)b c d
+
3 3 2    4 4
(4 a - 3)b c d  - b c d
*
- b x - a
%e
/
7       6
d x + c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^3, x)
(78)
4      3       2  2 6         3       2         3   5
(a  - 8 a  + 12 a )b d  + (- 4 a  + 24 a  - 24 a)b c d
+
2              4 2 4               5 3 3    6 4 2
(6 a  - 24 a + 12)b c d  + (- 4 a + 8)b c d  + b c d
*
2
x
+
4       3       2  2   5         3       2         3 2 4
(2 a  - 16 a  + 24 a )b c d  + (- 8 a  + 48 a  - 48 a)b c d
+
2              4 3 3                5 4 2      6 5
(12 a  - 48 a + 24)b c d  + (- 8 a + 16)b c d  + 2 b c d
*
x
+
4      3       2  2 2 4         3       2         3 3 3
(a  - 8 a  + 12 a )b c d  + (- 4 a  + 24 a  - 24 a)b c d
+
2              4 4 2               5 5     6 6
(6 a  - 24 a + 12)b c d  + (- 4 a + 8)b c d + b c
*
- a d + b c
-----------
- b d x - b c        d
Ei(-------------)%e
d
+
3 6 3                2 6      3   5  2
- 2 b d x  + ((- 8 a - 2)b d  + 2 b c d )x
+
4      3    6         3       2             2   5
(a  - 8 a )b d  + (- 4 a  + 24 a  - 16 a - 4)b c d
+
2              3 2 4               4 3 3    5 4 2
(6 a  - 24 a + 10)b c d  + (- 4 a + 8)b c d  + b c d
*
x
+
4 6     4      3      5         3       2            2 2 4
- a d  + (a  - 4 a )b c d  + (- 4 a  + 18 a  - 8 a - 2)b c d
+
2             3 3 3               4 4 2    5 5
(6 a  - 20 a + 6)b c d  + (- 4 a + 7)b c d  + b c d
*
- b x - a
%e
/
9 2        8       2 7
2 d x  + 4 c d x + 2 c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^4, x)
(79)
4       3       2         3 7
(- a  + 12 a  - 36 a  + 24 a)b d
+
3       2              4   6         2              5 2 5
(4 a  - 36 a  + 72 a - 24)b c d  + (- 6 a  + 36 a - 36)b c d
+
6 3 4    7 4 3
(4 a - 12)b c d  - b c d
*
3
x
+
4       3        2         3   6
(- 3 a  + 36 a  - 108 a  + 72 a)b c d
+
3        2               4 2 5
(12 a  - 108 a  + 216 a - 72)b c d
+
2                5 3 4               6 4 3      7 5 2
(- 18 a  + 108 a - 108)b c d  + (12 a - 36)b c d  - 3 b c d
*
2
x
+
4       3        2         3 2 5
(- 3 a  + 36 a  - 108 a  + 72 a)b c d
+
3        2               4 3 4
(12 a  - 108 a  + 216 a - 72)b c d
+
2                5 4 3               6 5 2      7 6
(- 18 a  + 108 a - 108)b c d  + (12 a - 36)b c d  - 3 b c d
*
x
+
4       3       2         3 3 4
(- a  + 12 a  - 36 a  + 24 a)b c d
+
3       2              4 4 3         2              5 5 2
(4 a  - 36 a  + 72 a - 24)b c d  + (- 6 a  + 36 a - 36)b c d
+
6 6     7 7
(4 a - 12)b c d - b c
*
- a d + b c
-----------
- b d x - b c        d
Ei(-------------)%e
d
+
3 7 3
- 6 b d x
+
4       3       2  2 7       3       2              3   6
(- a  + 12 a  - 36 a )b d  + (4 a  - 36 a  + 72 a - 18)b c d
+
2              4 2 5              5 3 4    6 4 3
(- 6 a  + 36 a - 36)b c d  + (4 a - 12)b c d  - b c d
*
2
x
+
4       3    7         4       3       2  2   6
(a  - 12 a )b d  + (- 2 a  + 20 a  - 36 a )b c d
+
3       2               3 2 5          2              4 3 4
(8 a  - 66 a  + 108 a - 18)b c d  + (- 12 a  + 68 a - 60)b c d
+
5 4 3      6 5 2
(8 a - 23)b c d  - 2 b c d
*
x
+
4 7     4      3      6       4      3       2  2 2 5
- 2 a d  + (a  - 4 a )b c d  + (- a  + 8 a  - 12 a )b c d
+
3       2             3 3 4         2              4 4 3
(4 a  - 30 a  + 44 a - 6)b c d  + (- 6 a  + 32 a - 26)b c d
+
5 5 2    6 6
(4 a - 11)b c d  - b c d
*
- b x - a
%e
/
11 3         10 2       2 9       3 8
6 d  x  + 18 c d  x  + 18 c d x + 6 c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^5, x)
(80)
4       3       2              4 8
(a  - 16 a  + 72 a  - 96 a + 24)b d
+
3       2               5   7       2              6 2 6
(- 4 a  + 48 a  - 144 a + 96)b c d  + (6 a  - 48 a + 72)b c d
+
7 3 5    8 4 4
(- 4 a + 16)b c d  + b c d
*
4
x
+
4       3        2               4   7
(4 a  - 64 a  + 288 a  - 384 a + 96)b c d
+
3        2                5 2 6
(- 16 a  + 192 a  - 576 a + 384)b c d
+
2                6 3 5                 7 4 4      8 5 3
(24 a  - 192 a + 288)b c d  + (- 16 a + 64)b c d  + 4 b c d
*
3
x
+
4       3        2                4 2 6
(6 a  - 96 a  + 432 a  - 576 a + 144)b c d
+
3        2                5 3 5
(- 24 a  + 288 a  - 864 a + 576)b c d
+
2                6 4 4                 7 5 3      8 6 2
(36 a  - 288 a + 432)b c d  + (- 24 a + 96)b c d  + 6 b c d
*
2
x
+
4       3        2               4 3 5
(4 a  - 64 a  + 288 a  - 384 a + 96)b c d
+
3        2                5 4 4
(- 16 a  + 192 a  - 576 a + 384)b c d
+
2                6 5 3                 7 6 2      8 7
(24 a  - 192 a + 288)b c d  + (- 16 a + 64)b c d  + 4 b c d
*
x
+
4       3       2              4 4 4
(a  - 16 a  + 72 a  - 96 a + 24)b c d
+
3       2               5 5 3       2              6 6 2
(- 4 a  + 48 a  - 144 a + 96)b c d  + (6 a  - 48 a + 72)b c d
+
7 7     8 8
(- 4 a + 16)b c d + b c
*
- a d + b c
-----------
- b d x - b c        d
Ei(-------------)%e
d
+
4       3       2         3 8
(a  - 16 a  + 72 a  - 96 a)b d
+
3       2               4   7       2              5 2 6
(- 4 a  + 48 a  - 144 a + 96)b c d  + (6 a  - 48 a + 72)b c d
+
6 3 5    7 4 4
(- 4 a + 16)b c d  + b c d
*
3
x
+
4       3       2  2 8
(- a  + 16 a  - 72 a )b d
+
4       3        2          3   7
(3 a  - 44 a  + 168 a  - 144 a)b c d
+
3        2                4 2 6
(- 12 a  + 138 a  - 384 a + 216)b c d
+
2                5 3 5                 6 4 4      7 5 3
(18 a  - 140 a + 200)b c d  + (- 12 a + 47)b c d  + 3 b c d
*
2
x
+
4       3    8         4       3       2  2   7
(2 a  - 32 a )b d  + (- 2 a  + 24 a  - 48 a )b c d
+
4       3        2         3 2 6
(3 a  - 40 a  + 132 a  - 96 a)b c d
+
3        2                4 3 5
(- 12 a  + 132 a  - 344 a + 176)b c d
+
2                5 4 4                 6 5 3      7 6 2
(18 a  - 136 a + 186)b c d  + (- 12 a + 46)b c d  + 3 b c d
*
x
+
4 8       4      3      7       4      3       2  2 2 6
- 6 a d  + (2 a  - 8 a )b c d  + (- a  + 8 a  - 12 a )b c d
+
4       3       2         3 3 5
(a  - 12 a  + 36 a  - 24 a)b c d
+
3       2               4 4 4       2              5 5 3
(- 4 a  + 42 a  - 104 a + 50)b c d  + (6 a  - 44 a + 58)b c d
+
6 6 2    7 7
(- 4 a + 15)b c d  + b c d
*
- b x - a
%e
/
13 4         12 3        2 11 2       3 10        4 9
24 d  x  + 96 c d  x  + 144 c d  x  + 96 c d  x + 24 c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
-- Integrands of the form x^m F(c (a+b x)) Logintegrate(d x] (e+(f+g x) Log[d x])
integrate(F^(c*(a+b*x))*x^m*log(d*x)^n*(e+e*n+e*(1+m+b*c*x*log(F))*log(d*x)), x)
(81)
(b c x + a c)log(F)  m log(x)
(e x log(x) + e x log(d))%e                   %e
*
n log(log(x) + log(d))
%e
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (OT) = 0.03 sec
integrate(F^(c*(a+b*x))*x^2*log(d*x)^n*(e+e*n+e*(3+b*c*x*log(F))*log(d*x)), x)
3          (b c x + a c)log(F)  n log(log(d x))
(82)  e x log(d x)%e                   %e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*x*log(d*x)^n*(e+e*n+e*(2+b*c*x*log(F))*log(d*x)), x)
2          (b c x + a c)log(F)  n log(log(d x))
(83)  e x log(d x)%e                   %e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+e*(1+b*c*x*log(F))*log(d*x)), x)
(b c x + a c)log(F)  n log(log(d x))
(84)  e x log(d x)%e                   %e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+b*c*e*x*log(F)*log(d*x))/x, x)
(b c x + a c)log(F)  n log(log(d x))
(85)  e log(d x)%e                   %e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+e*(-1+b*c*x*log(F))*log(d*x))/x^2, x)
(b c x + a c)log(F)  n log(log(d x))
e log(d x)%e                   %e
(86)  ------------------------------------------------
x
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+e*(-2+b*c*x*log(F))*log(d*x))/x^3, x)
(b c x + a c)log(F)  n log(log(d x))
e log(d x)%e                   %e
(87)  ------------------------------------------------
2
x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- Integrands of the form x^m F^(a+b x^n)
-- n>0
integrate(f^(a+b*x^2)*x^m, x)
(- m + 1)log(- b log(f)) + 2 a log(f)
-------------------------------------
m + 1      2                           2
Gamma(-----,- b x log(f))%e
2
(88)  ----------------------------------------------------------------
2 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^11, x)
(89)
5 10      5      4 8      4       3 6      3       2 4      2
b x  log(f)  - 5 b x log(f)  + 20 b x log(f)  - 60 b x log(f)
+
2
120 b x log(f) - 120
*
2
(b x  + a)log(f)
%e
/
6      6
2 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^9, x)
(90)
4 8      4      3 6      3       2 4      2         2
(b x log(f)  - 4 b x log(f)  + 12 b x log(f)  - 24 b x log(f) + 24)
*
2
(b x  + a)log(f)
%e
/
5      5
2 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^7, x)
2
3 6      3      2 4      2        2             (b x  + a)log(f)
(b x log(f)  - 3 b x log(f)  + 6 b x log(f) - 6)%e
(91)  ------------------------------------------------------------------
4      4
2 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^5, x)
2
2 4      2        2             (b x  + a)log(f)
(b x log(f)  - 2 b x log(f) + 2)%e
(92)  --------------------------------------------------
3      3
2 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^3, x)
2
2             (b x  + a)log(f)
(b x log(f) - 1)%e
(93)  ----------------------------------
2      2
2 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x, x)
2
(b x  + a)log(f)
%e
(94)  ------------------
2 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^2)/x, x)
2         a log(f)
Ei(b x log(f))%e
(95)  ------------------------
2
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^3, x)
2
(b x  + a)log(f)      2            2         a log(f)
- %e                 + b x log(f)Ei(b x log(f))%e
(96)  ---------------------------------------------------------
2
2 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^5, x)
(97)
2
2             (b x  + a)log(f)    2 4      2      2         a log(f)
(- b x log(f) - 1)%e                 + b x log(f) Ei(b x log(f))%e
--------------------------------------------------------------------------
4
4 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^7, x)
(98)
2
2 4      2      2             (b x  + a)log(f)
(- b x log(f)  - b x log(f) - 2)%e
+
3 6      3      2         a log(f)
b x log(f) Ei(b x log(f))%e
/
6
12 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^9, x)
(99)
2
3 6      3    2 4      2        2             (b x  + a)log(f)
(- b x log(f)  - b x log(f)  - 2 b x log(f) - 6)%e
+
4 8      4      2         a log(f)
b x log(f) Ei(b x log(f))%e
/
8
48 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^11, x)
(100)
4 8      4    3 6      3      2 4      2        2
(- b x log(f)  - b x log(f)  - 2 b x log(f)  - 6 b x log(f) - 24)
*
2
(b x  + a)log(f)
%e
+
5 10      5      2         a log(f)
b x  log(f) Ei(b x log(f))%e
/
10
240 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^12, x)
(101)
+---+  a log(f)      +----------+
10395 \|%pi %e        erf(x\|- b log(f) )
+
5 11      5        4 9      4         3 7      3
64 b x  log(f)  - 352 b x log(f)  + 1584 b x log(f)
+
2 5      2            3
- 5544 b x log(f)  + 13860 b x log(f) - 20790 x
*
2
(b x  + a)log(f) +----------+
%e                \|- b log(f)
/
6      6 +----------+
128 b log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^10, x)
(102)
+---+  a log(f)      +----------+
- 945 \|%pi %e        erf(x\|- b log(f) )
+
4 9      4        3 7      3        2 5      2           3
32 b x log(f)  - 144 b x log(f)  + 504 b x log(f)  - 1260 b x log(f)
+
1890 x
*
2
(b x  + a)log(f) +----------+
%e                \|- b log(f)
/
5      5 +----------+
64 b log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^8, x)
(103)
+---+  a log(f)      +----------+
105 \|%pi %e        erf(x\|- b log(f) )
+
3 7      3       2 5      2          3
(16 b x log(f)  - 56 b x log(f)  + 140 b x log(f) - 210 x)
*
2
(b x  + a)log(f) +----------+
%e                \|- b log(f)
/
4      4 +----------+
32 b log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^6, x)
(104)
+---+  a log(f)      +----------+
- 15 \|%pi %e        erf(x\|- b log(f) )
+
2
2 5      2         3                (b x  + a)log(f) +----------+
(8 b x log(f)  - 20 b x log(f) + 30 x)%e                \|- b log(f)
/
3      3 +----------+
16 b log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^2)*x^4, x)
(105)
+---+  a log(f)      +----------+
3 \|%pi %e        erf(x\|- b log(f) )
+
2
3               (b x  + a)log(f) +----------+
(4 b x log(f) - 6 x)%e                \|- b log(f)
/
2      2 +----------+
8 b log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^2, x)
(106)
2
+---+  a log(f)      +----------+          (b x  + a)log(f) +----------+
- \|%pi %e        erf(x\|- b log(f) ) + 2 x %e                \|- b log(f)
---------------------------------------------------------------------------
+----------+
4 b log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2), x)
+---+  a log(f)      +----------+
\|%pi %e        erf(x\|- b log(f) )
(107)  -----------------------------------
+----------+
2 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^2, x)
(108)
+---+  a log(f)      +----------+
b x log(f)\|%pi %e        erf(x\|- b log(f) )
+
2
(b x  + a)log(f) +----------+
- %e                \|- b log(f)
/
+----------+
x\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^4, x)
(109)
2 3      2 +---+  a log(f)      +----------+
2 b x log(f) \|%pi %e        erf(x\|- b log(f) )
+
2
2             (b x  + a)log(f) +----------+
(- 2 b x log(f) - 1)%e                \|- b log(f)
/
3 +----------+
3 x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^6, x)
(110)
3 5      3 +---+  a log(f)      +----------+
4 b x log(f) \|%pi %e        erf(x\|- b log(f) )
+
2
2 4      2        2             (b x  + a)log(f) +----------+
(- 4 b x log(f)  - 2 b x log(f) - 3)%e                \|- b log(f)
/
5 +----------+
15 x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^2)/x^8, x)
(111)
4 7      4 +---+  a log(f)      +----------+
8 b x log(f) \|%pi %e        erf(x\|- b log(f) )
+
2
3 6      3      2 4      2        2              (b x  + a)log(f)
(- 8 b x log(f)  - 4 b x log(f)  - 6 b x log(f) - 15)%e
*
+----------+
\|- b log(f)
/
7 +----------+
105 x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^10, x)
(112)
5 9      5 +---+  a log(f)      +----------+
16 b x log(f) \|%pi %e        erf(x\|- b log(f) )
+
4 8      4      3 6      3       2 4      2         2
- 16 b x log(f)  - 8 b x log(f)  - 12 b x log(f)  - 30 b x log(f)
+
- 105
*
2
(b x  + a)log(f) +----------+
%e                \|- b log(f)
/
9 +----------+
945 x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^2)/x^12, x)
(113)
6 11      6 +---+  a log(f)      +----------+
32 b x  log(f) \|%pi %e        erf(x\|- b log(f) )
+
5 10      5       4 8      4       3 6      3       2 4      2
- 32 b x  log(f)  - 16 b x log(f)  - 24 b x log(f)  - 60 b x log(f)
+
2
- 210 b x log(f) - 945
*
2
(b x  + a)log(f) +----------+
%e                \|- b log(f)
/
11 +----------+
10395 x  \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^m, x)
(- m + 2)log(- b log(f)) + 3 a log(f)
-------------------------------------
m + 1      3                           3
Gamma(-----,- b x log(f))%e
3
(114)  ----------------------------------------------------------------
3 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^17, x)
(115)
5 15      5      4 12      4       3 9      3       2 6      2
b x  log(f)  - 5 b x  log(f)  + 20 b x log(f)  - 60 b x log(f)
+
3
120 b x log(f) - 120
*
3
(b x  + a)log(f)
%e
/
6      6
3 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(a+b*x^3)*x^14, x)
(116)
4 12      4      3 9      3       2 6      2         3
(b x  log(f)  - 4 b x log(f)  + 12 b x log(f)  - 24 b x log(f) + 24)
*
3
(b x  + a)log(f)
%e
/
5      5
3 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^11, x)
3
3 9      3      2 6      2        3             (b x  + a)log(f)
(b x log(f)  - 3 b x log(f)  + 6 b x log(f) - 6)%e
(117)  ------------------------------------------------------------------
4      4
3 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^8, x)
3
2 6      2        3             (b x  + a)log(f)
(b x log(f)  - 2 b x log(f) + 2)%e
(118)  --------------------------------------------------
3      3
3 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^5, x)
3
3             (b x  + a)log(f)
(b x log(f) - 1)%e
(119)  ----------------------------------
2      2
3 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^2, x)
3
(b x  + a)log(f)
%e
(120)  ------------------
3 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x, x)
3         a log(f)
Ei(b x log(f))%e
(121)  ------------------------
3
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x^4, x)
3
(b x  + a)log(f)      3            3         a log(f)
- %e                 + b x log(f)Ei(b x log(f))%e
(122)  ---------------------------------------------------------
3
3 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x^7, x)
(123)
3
3             (b x  + a)log(f)    2 6      2      3         a log(f)
(- b x log(f) - 1)%e                 + b x log(f) Ei(b x log(f))%e
--------------------------------------------------------------------------
6
6 x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^3)/x^10, x)
(124)
3
2 6      2      3             (b x  + a)log(f)
(- b x log(f)  - b x log(f) - 2)%e
+
3 9      3      3         a log(f)
b x log(f) Ei(b x log(f))%e
/
9
18 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x^13, x)
(125)
3
3 9      3    2 6      2        3             (b x  + a)log(f)
(- b x log(f)  - b x log(f)  - 2 b x log(f) - 6)%e
+
4 12      4      3         a log(f)
b x  log(f) Ei(b x log(f))%e
/
12
72 x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^3)/x^16, x)
(126)
4 12      4    3 9      3      2 6      2        3
(- b x  log(f)  - b x log(f)  - 2 b x log(f)  - 6 b x log(f) - 24)
*
3
(b x  + a)log(f)
%e
+
5 15      5      3         a log(f)
b x  log(f) Ei(b x log(f))%e
/
15
360 x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^4, x)
(127)
3
2  (b x  + a)log(f) 3+----------+2       a log(f)      2      3
3 x %e                 \|- b log(f)   + 2 %e        Gamma(-,- b x log(f))
3
-------------------------------------------------------------------------
3+----------+2
9 b log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^3, x)
(128)
3
(b x  + a)log(f) 3+----------+     a log(f)      1      3
3 x %e                 \|- b log(f)  + %e        Gamma(-,- b x log(f))
3
----------------------------------------------------------------------
3+----------+
9 b log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^3)*x, x)
a log(f)      2      3
%e        Gamma(-,- b x log(f))
3
(129)  - -------------------------------
3+----------+2
3 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3), x)
a log(f)      1      3
%e        Gamma(-,- b x log(f))
3
(130)  - -------------------------------
3+----------+
3 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x^2, x)
(131)
3
(b x  + a)log(f) 3+----------+2
- %e                 \|- b log(f)
+
a log(f)      2      3
- b x log(f)%e        Gamma(-,- b x log(f))
3
/
3+----------+2
x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x^3, x)
(132)
3
(b x  + a)log(f) 3+----------+
- %e                 \|- b log(f)
+
2        a log(f)      1      3
- b x log(f)%e        Gamma(-,- b x log(f))
3
/
2 3+----------+
2 x  \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(%e^(4*x^3)*x^2, x)
3
4 x
%e
(133)  ------
12
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- n<0
integrate(f^(a+b/x)*x^m, x)
b + %A a
x     --------
++    m    %A
(134)   |   %A f        d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)*x^4, x)
(135)
4        4    3 2      3      2 3      2        4             5
(b x log(f)  + b x log(f)  + 2 b x log(f)  + 6 b x log(f) + 24 x )
*
(a x + b)log(f)
---------------
x
%e
+
5      5   b log(f)   a log(f)
- b log(f) Ei(--------)%e
x
/
120
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)*x^3, x)
(136)
(a x + b)log(f)
---------------
3        3    2 2      2        3            4          x
(b x log(f)  + b x log(f)  + 2 b x log(f) + 6 x )%e
+
4      4   b log(f)   a log(f)
- b log(f) Ei(--------)%e
x
/
24
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)*x^2, x)
(137)
(a x + b)log(f)
---------------
2        2      2            3          x
(b x log(f)  + b x log(f) + 2 x )%e
+
3      3   b log(f)   a log(f)
- b log(f) Ei(--------)%e
x
/
6
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)*x, x)
(a x + b)log(f)
---------------
2          x           2      2   b log(f)   a log(f)
(b x log(f) + x )%e                - b log(f) Ei(--------)%e
x
(138)  --------------------------------------------------------------------
2
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x), x)
(a x + b)log(f)
---------------
x                     b log(f)   a log(f)
(139)  x %e                - b log(f)Ei(--------)%e
x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)/x, x)
b log(f)   a log(f)
(140)  - Ei(--------)%e
x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x)/x^2, x)
(a x + b)log(f)
---------------
x
%e
(141)  - -----------------
b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)/x^3, x)
(a x + b)log(f)
---------------
x
(- b log(f) + x)%e
(142)  ---------------------------------
2        2
b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)/x^4, x)
(a x + b)log(f)
---------------
2      2                     2          x
(- b log(f)  + 2 b x log(f) - 2 x )%e
(143)  ----------------------------------------------------
3 2      3
b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x)/x^5, x)
(a x + b)log(f)
---------------
3      3      2        2        2            3          x
(- b log(f)  + 3 b x log(f)  - 6 b x log(f) + 6 x )%e
(144)  --------------------------------------------------------------------
4 3      4
b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)/x^6, x)
(145)
4      4      3        3       2 2      2         3             4
(- b log(f)  + 4 b x log(f)  - 12 b x log(f)  + 24 b x log(f) - 24 x )
*
(a x + b)log(f)
---------------
x
%e
/
5 4      5
b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x)/x^7, x)
(146)
5      5      4        4       3 2      3       2 3      2
- b log(f)  + 5 b x log(f)  - 20 b x log(f)  + 60 b x log(f)
+
4              5
- 120 b x log(f) + 120 x
*
(a x + b)log(f)
---------------
x
%e
/
6 5      6
b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)*x^m, x)
2
b + %A a
--------
x          2
++    m    %A
(147)   |   %A f        d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)*x^9, x)
(148)
4 2      4    3 4      3      2 6      2        8             10
(b x log(f)  + b x log(f)  + 2 b x log(f)  + 6 b x log(f) + 24 x  )
*
2
(a x  + b)log(f)
----------------
2
x
%e
+
5      5   b log(f)   a log(f)
- b log(f) Ei(--------)%e
2
x
/
240
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)*x^7, x)
(149)
2
(a x  + b)log(f)
----------------
2
3 2      3    2 4      2        6            8          x
(b x log(f)  + b x log(f)  + 2 b x log(f) + 6 x )%e
+
4      4   b log(f)   a log(f)
- b log(f) Ei(--------)%e
2
x
/
48
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)*x^5, x)
(150)
2
(a x  + b)log(f)
----------------
2
2 2      2      4            6          x
(b x log(f)  + b x log(f) + 2 x )%e
+
3      3   b log(f)   a log(f)
- b log(f) Ei(--------)%e
2
x
/
12
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)*x^3, x)
(151)
2
(a x  + b)log(f)
----------------
2
2          4          x            2      2   b log(f)   a log(f)
(b x log(f) + x )%e                 - b log(f) Ei(--------)%e
2
x
---------------------------------------------------------------------
4
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)*x, x)
2
(a x  + b)log(f)
----------------
2
2         x                      b log(f)   a log(f)
x %e                 - b log(f)Ei(--------)%e
2
x
(152)  -----------------------------------------------------
2
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x, x)
b log(f)   a log(f)
Ei(--------)%e
2
x
(153)  - ----------------------
2
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^3, x)
2
(a x  + b)log(f)
----------------
2
x
%e
(154)  - ------------------
2 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^5, x)
2
(a x  + b)log(f)
----------------
2
2          x
(- b log(f) + x )%e
(155)  -----------------------------------
2 2      2
2 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^7, x)
2
(a x  + b)log(f)
----------------
2
2      2        2            4          x
(- b log(f)  + 2 b x log(f) - 2 x )%e
(156)  -----------------------------------------------------
3 4      3
2 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^9, x)
(157)
2
(a x  + b)log(f)
----------------
2
3      3      2 2      2        4            6          x
(- b log(f)  + 3 b x log(f)  - 6 b x log(f) + 6 x )%e
---------------------------------------------------------------------
4 6      4
2 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^11, x)
(158)
4      4      3 2      3       2 4      2         6             8
(- b log(f)  + 4 b x log(f)  - 12 b x log(f)  + 24 b x log(f) - 24 x )
*
2
(a x  + b)log(f)
----------------
2
x
%e
/
5 8      5
2 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^13, x)
(159)
5      5      4 2      4       3 4      3       2 6      2
- b log(f)  + 5 b x log(f)  - 20 b x log(f)  + 60 b x log(f)
+
8              10
- 120 b x log(f) + 120 x
*
2
(a x  + b)log(f)
----------------
2
x
%e
/
6 10      6
2 b x  log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)*x^10, x)
(160)
+----------+
6      6 +---+  a log(f)    \|- b log(f)
- 32 b log(f) \|%pi %e        erf(-------------)
x
+
5        5       4 3      4       3 5      3       2 7      2
32 b x log(f)  + 16 b x log(f)  + 24 b x log(f)  + 60 b x log(f)
+
9              11
210 b x log(f) + 945 x
*
2
(a x  + b)log(f)
----------------
2
x         +----------+
%e                \|- b log(f)
/
+----------+
10395 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)*x^8, x)
(161)
+----------+
5      5 +---+  a log(f)    \|- b log(f)
- 16 b log(f) \|%pi %e        erf(-------------)
x
+
4        4      3 3      3       2 5      2         7
16 b x log(f)  + 8 b x log(f)  + 12 b x log(f)  + 30 b x log(f)
+
9
105 x
*
2
(a x  + b)log(f)
----------------
2
x         +----------+
%e                \|- b log(f)
/
+----------+
945 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)*x^6, x)
(162)
+----------+
4      4 +---+  a log(f)    \|- b log(f)
- 8 b log(f) \|%pi %e        erf(-------------)
x
+
3        3      2 3      2        5             7
(8 b x log(f)  + 4 b x log(f)  + 6 b x log(f) + 15 x )
*
2
(a x  + b)log(f)
----------------
2
x         +----------+
%e                \|- b log(f)
/
+----------+
105 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)*x^4, x)
(163)
+----------+
3      3 +---+  a log(f)    \|- b log(f)
- 4 b log(f) \|%pi %e        erf(-------------)
x
+
2
(a x  + b)log(f)
----------------
2
2        2        3            5          x         +----------+
(4 b x log(f)  + 2 b x log(f) + 3 x )%e                \|- b log(f)
/
+----------+
15 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)*x^2, x)
(164)
+----------+
2      2 +---+  a log(f)    \|- b log(f)
- 2 b log(f) \|%pi %e        erf(-------------)
x
+
2
(a x  + b)log(f)
----------------
2
3          x         +----------+
(2 b x log(f) + x )%e                \|- b log(f)
/
+----------+
3 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(a+b/x^2), x)
(165)
+----------+
+---+  a log(f)    \|- b log(f)
- b log(f)\|%pi %e        erf(-------------)
x
+
2
(a x  + b)log(f)
----------------
2
x         +----------+
x %e                \|- b log(f)
/
+----------+
\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^2, x)
+----------+
+---+  a log(f)    \|- b log(f)
\|%pi %e        erf(-------------)
x
(166)  - ----------------------------------
+----------+
2 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^4, x)
(167)
2
(a x  + b)log(f)
----------------
+----------+                2
+---+  a log(f)    \|- b log(f)                x         +----------+
x\|%pi %e        erf(-------------) - 2 %e                \|- b log(f)
x
-----------------------------------------------------------------------
+----------+
4 b x log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^6, x)
(168)
+----------+
3 +---+  a log(f)    \|- b log(f)
- 3 x \|%pi %e        erf(-------------)
x
+
2
(a x  + b)log(f)
----------------
2
2          x         +----------+
(- 4 b log(f) + 6 x )%e                \|- b log(f)
/
2 3      2 +----------+
8 b x log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^8, x)
(169)
+----------+
5 +---+  a log(f)    \|- b log(f)
15 x \|%pi %e        erf(-------------)
x
+
2
(a x  + b)log(f)
----------------
2
2      2         2             4          x         +----------+
(- 8 b log(f)  + 20 b x log(f) - 30 x )%e                \|- b log(f)
/
3 5      3 +----------+
16 b x log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^10, x)
(170)
+----------+
7 +---+  a log(f)    \|- b log(f)
- 105 x \|%pi %e        erf(-------------)
x
+
3      3       2 2      2          4              6
(- 16 b log(f)  + 56 b x log(f)  - 140 b x log(f) + 210 x )
*
2
(a x  + b)log(f)
----------------
2
x         +----------+
%e                \|- b log(f)
/
4 7      4 +----------+
32 b x log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^12, x)
(171)
+----------+
9 +---+  a log(f)    \|- b log(f)
945 x \|%pi %e        erf(-------------)
x
+
4      4        3 2      3        2 4      2           6
- 32 b log(f)  + 144 b x log(f)  - 504 b x log(f)  + 1260 b x log(f)
+
8
- 1890 x
*
2
(a x  + b)log(f)
----------------
2
x         +----------+
%e                \|- b log(f)
/
5 9      5 +----------+
64 b x log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^14, x)
(172)
+----------+
11 +---+  a log(f)    \|- b log(f)
- 10395 x  \|%pi %e        erf(-------------)
x
+
5      5        4 2      4         3 4      3
- 64 b log(f)  + 352 b x log(f)  - 1584 b x log(f)
+
2 6      2            8                10
5544 b x log(f)  - 13860 b x log(f) + 20790 x
*
2
(a x  + b)log(f)
----------------
2
x         +----------+
%e                \|- b log(f)
/
6 11      6 +----------+
128 b x  log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)*x^m, x)
3
b + %A a
--------
x          3
++    m    %A
(173)   |   %A f        d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)*x^14, x)
(174)
4 3      4    3 6      3      2 9      2        12             15
(b x log(f)  + b x log(f)  + 2 b x log(f)  + 6 b x  log(f) + 24 x  )
*
3
(a x  + b)log(f)
----------------
3
x
%e
+
5      5   b log(f)   a log(f)
- b log(f) Ei(--------)%e
3
x
/
360
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)*x^11, x)
(175)
3
(a x  + b)log(f)
----------------
3
3 3      3    2 6      2        9            12          x
(b x log(f)  + b x log(f)  + 2 b x log(f) + 6 x  )%e
+
4      4   b log(f)   a log(f)
- b log(f) Ei(--------)%e
3
x
/
72
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)*x^8, x)
(176)
3
(a x  + b)log(f)
----------------
3
2 3      2      6            9          x
(b x log(f)  + b x log(f) + 2 x )%e
+
3      3   b log(f)   a log(f)
- b log(f) Ei(--------)%e
3
x
/
18
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)*x^5, x)
(177)
3
(a x  + b)log(f)
----------------
3
3          6          x            2      2   b log(f)   a log(f)
(b x log(f) + x )%e                 - b log(f) Ei(--------)%e
3
x
---------------------------------------------------------------------
6
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)*x^2, x)
3
(a x  + b)log(f)
----------------
3
3         x                      b log(f)   a log(f)
x %e                 - b log(f)Ei(--------)%e
3
x
(178)  -----------------------------------------------------
3
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)/x, x)
b log(f)   a log(f)
Ei(--------)%e
3
x
(179)  - ----------------------
3
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x^4, x)
3
(a x  + b)log(f)
----------------
3
x
%e
(180)  - ------------------
3 b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x^7, x)
3
(a x  + b)log(f)
----------------
3
3          x
(- b log(f) + x )%e
(181)  -----------------------------------
2 3      2
3 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)/x^10, x)
3
(a x  + b)log(f)
----------------
3
2      2        3            6          x
(- b log(f)  + 2 b x log(f) - 2 x )%e
(182)  -----------------------------------------------------
3 6      3
3 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x^13, x)
(183)
3
(a x  + b)log(f)
----------------
3
3      3      2 3      2        6            9          x
(- b log(f)  + 3 b x log(f)  - 6 b x log(f) + 6 x )%e
---------------------------------------------------------------------
4 9      4
3 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x^16, x)
(184)
4      4      3 3      3       2 6      2         9             12
(- b log(f)  + 4 b x log(f)  - 12 b x log(f)  + 24 b x log(f) - 24 x  )
*
3
(a x  + b)log(f)
----------------
3
x
%e
/
5 12      5
3 b x  log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x^19, x)
(185)
5      5      4 3      4       3 6      3       2 9      2
- b log(f)  + 5 b x log(f)  - 20 b x log(f)  + 60 b x log(f)
+
12              15
- 120 b x  log(f) + 120 x
*
3
(a x  + b)log(f)
----------------
3
x
%e
/
6 15      6
3 b x  log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)*x^4, x)
(186)
3
(a x  + b)log(f)
----------------
3
2            5          x         3+----------+
(3 b x log(f) + 2 x )%e                 \|- b log(f)
+
2      2  a log(f)      1   b log(f)
3 b log(f) %e        Gamma(-,- --------)
3       3
x
/
3+----------+
10 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)*x^3, x)
(187)
3
(a x  + b)log(f)
----------------
3
4          x         3+----------+2
(3 b x log(f) + x )%e                 \|- b log(f)
+
2      2  a log(f)      2   b log(f)
3 b log(f) %e        Gamma(-,- --------)
3       3
x
/
3+----------+2
4 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)*x, x)
(188)
3
(a x  + b)log(f)
----------------
3
2         x         3+----------+             a log(f)      1   b log(f)
x %e                 \|- b log(f)  + b log(f)%e        Gamma(-,- --------)
3       3
x
--------------------------------------------------------------------------
3+----------+
2 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3), x)
(189)
3
(a x  + b)log(f)
----------------
3
x         3+----------+2             a log(f)      2   b log(f)
x %e                 \|- b log(f)   + b log(f)%e        Gamma(-,- --------)
3       3
x
---------------------------------------------------------------------------
3+----------+2
\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(a+b/x^3)/x^2, x)
a log(f)      1   b log(f)
%e        Gamma(-,- --------)
3       3
x
(190)  -----------------------------
3+----------+
3 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)/x^3, x)
a log(f)      2   b log(f)
%e        Gamma(-,- --------)
3       3
x
(191)  -----------------------------
3+----------+2
3 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x^5, x)
(192)
3
(a x  + b)log(f)
----------------
3
x         3+----------+       a log(f)      1   b log(f)
- 3 %e                 \|- b log(f)  - x %e        Gamma(-,- --------)
3       3
x
----------------------------------------------------------------------
3+----------+
9 b x log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- n symbolic
integrate(f^(a+b*x^n)*x^m, x)
x         n
++    m b %A  + a
(193)   |   %A f         d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(a+b*x^n)*x^3, x)
x         n
++    3 b %A  + a
(194)   |   %A f         d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)*x^2, x)
x         n
++    2 b %A  + a
(195)   |   %A f         d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)*x, x)
x         n
++      b %A  + a
(196)   |   %A f         d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n), x)
x      n
++   b %A  + a
(197)   |   f         d%A
++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)/x, x)
a log(f)             n log(x)
%e        Ei(b log(f)%e        )
(198)  --------------------------------
n
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)/x^2, x)
n
x  b %A  + a
++  f
(199)   |   ---------- d%A
++         2
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)/x^3, x)
n
x  b %A  + a
++  f
(200)   |   ---------- d%A
++         3
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)/x^4, x)
n
x  b %A  + a
++  f
(201)   |   ---------- d%A
++         4
%A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)*x^(-1+3*n), x)
(202)
2      2   n log(x) 2               n log(x)
(b log(f) (%e        )  - 2 b log(f)%e         + 2)
*
n log(x)
b log(f)%e         + a log(f)
%e
/
3        3
b n log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)*x^(-1+2*n), x)
n log(x)
n log(x)       b log(f)%e         + a log(f)
(b log(f)%e         - 1)%e
(203)  -------------------------------------------------------
2        2
b n log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)*x^(-1+n), x)
n log(x)
b log(f)%e         + a log(f)
%e
(204)  -------------------------------
b n log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)/x, x)
a log(f)             n log(x)
%e        Ei(b log(f)%e        )
(205)  --------------------------------
n
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)*x^(-1-n), x)
(206)
n log(x)
b log(f)%e         + a log(f)
- %e
+
a log(f)  n log(x)             n log(x)
b log(f)%e        %e        Ei(b log(f)%e        )
/
n log(x)
n %e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)*x^(-1-2*n), x)
(207)
n log(x)
n log(x)       b log(f)%e         + a log(f)
(- b log(f)%e         - 1)%e
+
2      2  a log(f)   n log(x) 2             n log(x)
b log(f) %e        (%e        ) Ei(b log(f)%e        )
/
n log(x) 2
2 n (%e        )
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)*x^(-1+5/2*n), x)
(208)
n log(x) 3       n log(x)
--------         --------
2                2     +----------+
(4 b log(f)(%e        )  - 6 %e        )\|- b log(f)
*
n log(x) 2
--------
2
b log(f)(%e        )  + a log(f)
%e
+
n log(x)
--------
+---+  a log(f)          2    +----------+
3 \|%pi %e        erf(%e        \|- b log(f) )
/
2        2 +----------+
4 b n log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.01 (EV) = 0.02 sec
integrate(f^(a+b*x^n)*x^(-1+3/2*n), x)
(209)
n log(x) 2
n log(x)                          --------
--------                              2
2    +----------+  b log(f)(%e        )  + a log(f)
2 %e        \|- b log(f) %e
+
n log(x)
--------
+---+  a log(f)          2    +----------+
- \|%pi %e        erf(%e        \|- b log(f) )
/
+----------+
2 b n log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)*x^(-1+1/2*n), x)
(n - 2)log(x)
-------------
+---+  a log(f)              2       +----------+
\|%pi %e        erf(x %e             \|- b log(f) )
(210)  ---------------------------------------------------
+----------+
n\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)*x^(-1-1/2*n), x)
(211)
-
(- n - 2)log(x)
---------------
2        +----------+
2 x %e               \|- b log(f)
*
(- n - 2)log(x) 2
---------------
2                2
a x log(f)(%e               )  + b log(f)
-----------------------------------------
(- n - 2)log(x) 2
---------------
2          2
x (%e               )
%e
+
+----------+
+---+  a log(f)       \|- b log(f)
2 b log(f)\|%pi %e        erf(-------------------)
(- n - 2)log(x)
---------------
2
x %e
/
+----------+
n\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(a+b*x^n)*x^(-1-3/2*n), x)
(212)
(- 3 n - 2)log(x) 3                   (- 3 n - 2)log(x)
-----------------                     -----------------
6                       3+-+          6
(- 2 x (%e                 )  - 4 b log(f)\|x %e                 )
*
(- 3 n - 2)log(x) 2
-----------------
3+-+2           6
a log(f)\|x  (%e                 )  + b log(f)
----------------------------------------------
(- 3 n - 2)log(x) 2
-----------------
3+-+2           6
+----------+            \|x  (%e                 )
\|- b log(f) %e
+
+----------+
2      2 +---+  a log(f)         \|- b log(f)
4 b log(f) \|%pi %e        erf(-----------------------)
(- 3 n - 2)log(x)
-----------------
3+-+          6
\|x %e
/
+----------+
3 n\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(%e^((-0.1)*x)*x, x)
There are 12 exposed and 10 unexposed library operations named
integrate having 2 argument(s) but none was determined to be
applicable. Use HyperDoc Browse, or issue
)display op integrate
Continuing to read the file...