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# Edit detail for FriCASTimofeev9 revision 2 of 2

 1 2 Editor: test1 Time: 2015/06/01 17:05:28 GMT+0 Note:

added:
Timofeev Chapter 9 Integration Problems

removed:
--- Timofeev Chapter 9 Integration Problems


Timofeev Chapter 9 Integration Problems

fricas
-- Problems 1 - 6 (p. 391-392)
integrate(acos(x)^2/x^5, x)
 (1)
Type: Union(Expression(Integer),...)
fricas
integrate(x^2*asin(x)^2, x)
 (2)
Type: Union(Expression(Integer),...)
fricas
integrate(x^3*atan(x)^2, x)
 (3)
Type: Union(Expression(Integer),...)
fricas
integrate(atan(x)^2/x^5, x)
 (4)
Type: Union(Expression(Integer),...)
fricas
integrate(x^3*acsc(x)^2, x)
 (5)
Type: Union(Expression(Integer),...)
fricas
integrate(asec(x)^4/x^5, x)
 (6)
Type: Union(Expression(Integer),...)
fricas
-- Problems 7 - 18 (p. 397-398)
integrate(asin(x)*sqrt(1-x^2), x)
 (7)
Type: Union(Expression(Integer),...)
fricas
integrate(acos(x)*sqrt(1-x^2), x)
 (8)
Type: Union(Expression(Integer),...)
fricas
integrate(x*acos(x)*sqrt(1-x^2), x)
 (9)
Type: Union(Expression(Integer),...)
fricas
integrate((1-x^2)^(3/2)*asin(x), x)
 (10)
Type: Union(Expression(Integer),...)
fricas
integrate(x*(1-x^2)^(3/2)*asin(x), x)
 (11)
Type: Union(Expression(Integer),...)
fricas
integrate(x^3*(1-x^2)^(3/2)*acos(x), x)
 (12)
Type: Union(Expression(Integer),...)
fricas
integrate((1-x^2)^(3/2)*acos(x)/x, x)
 (13)
Type: Union(Expression(Integer),...)
fricas
integrate((1-x^2)^(3/2)*asin(x)/x^6, x)
 (14)
Type: Union(Expression(Integer),...)
fricas
integrate(x^2*asin(x)/sqrt(1-x^2), x)
 (15)
Type: Union(Expression(Integer),...)
fricas
integrate(x^4*asin(x)/sqrt(1-x^2), x)
 (16)
Type: Union(Expression(Integer),...)
fricas
integrate(x*asin(x)/(1-x^2)^(3/2), x)
 (17)
Type: Union(Expression(Integer),...)
fricas
integrate(x*acos(x)/(1-x^2)^(3/2), x)
 (18)
Type: Union(Expression(Integer),...)
fricas
integrate(asin(x)/(1-x^2)^(5/2), x)
 (19)
Type: Union(Expression(Integer),...)
fricas
integrate(x^3*asin(x)/(1-x^2)^(3/2), x)
 (20)
Type: Union(Expression(Integer),...)
fricas
-- Problems 19 - 22 (p. 401)
integrate(asin(x)/(x*(1-x^2)^(3/2)), x)
 (21)
Type: Union(Expression(Integer),...)
fricas
integrate(acos(x)/(x^4*sqrt(1-x^2)), x)
 (22)
Type: Union(Expression(Integer),...)
fricas
integrate(x*acos(x)^2*sqrt(1-x^2), x)
 (23)
Type: Union(Expression(Integer),...)
fricas
integrate(x^2*asin(x)^3/sqrt(1-x^2), x)
 (24)
Type: Union(Expression(Integer),...)
fricas
-- Problems 23 - 26 (p. 404-405)
integrate(x*atan(x)/(1+x^2)^2, x)
 (25)
Type: Union(Expression(Integer),...)
fricas
integrate(x*atan(x)/(1+x^2)^3, x)
 (26)
Type: Union(Expression(Integer),...)
fricas
integrate(x^2*atan(x)/(1+x^2), x)
 (27)
Type: Union(Expression(Integer),...)
fricas
integrate(x^3*atan(x)/(1+x^2), x)
 (28)
Type: Union(Expression(Integer),...)
fricas
-- Problems 27 - 32 (p. 407-408)
integrate(x^2*atan(x)/(1+x^2)^2, x)
 (29)
Type: Union(Expression(Integer),...)
fricas
integrate(x^3*atan(x)/(1+x^2)^2, x)
 (30)
Type: Union(Expression(Integer),...)
fricas
integrate(x^5*atan(x)/(1+x^2)^2, x)
 (31)
Type: Union(Expression(Integer),...)
fricas
integrate((1+x^2)*atan(x)/x^2, x)
 (32)
Type: Union(Expression(Integer),...)
fricas
integrate((1+x^2)*atan(x)/x^5, x)
 (33)
Type: Union(Expression(Integer),...)
fricas
integrate((1+x^2)^2*atan(x)/x^5, x)
 (34)
Type: Union(Expression(Integer),...)
fricas
-- Problems 33 - 36 (p. 409)
integrate(atan(x)/(x^2*(1+x^2)), x)
 (35)
Type: Union(Expression(Integer),...)
fricas
integrate(atan(x)^2/x^3, x)
 (36)
Type: Union(Expression(Integer),...)
fricas
integrate((1+x^2)*atan(x)^2/x^5, x)
 (37)
Type: Union(Expression(Integer),...)
fricas
integrate(x^3*atan(x)^2/(1+x^2)^3, x)
 (38)
Type: Union(Expression(Integer),...)
fricas
-- Problems 37 - 43 (p. 412-414)
integrate(asec(x)*sqrt(-1+x^2)/x^2, x)
 (39)
Type: Union(Expression(Integer),...)
fricas
integrate((-1+x^2)^(5/2)*acsc(x)/x^3, x)
 (40)
Type: Union(Expression(Integer),...)
fricas
integrate(asec(x)*sqrt(-1+x^2)/x^4, x)
 (41)
Type: Union(Expression(Integer),...)
fricas
integrate(asec(x)/(-1+x^2)^(5/2), x)
 (42)
Type: Union(Expression(Integer),...)
fricas
integrate(x^2*asec(x)/(-1+x^2)^(5/2), x)
 (43)
Type: Union(Expression(Integer),...)
fricas
integrate(x^3*asec(x)/(-1+x^2)^(5/2), x)
 (44)
Type: Union(Expression(Integer),...)
fricas
integrate(x^6*asec(x)/(-1+x^2)^(5/2), x)
 (45)
Type: Union(Expression(Integer),...)
fricas
-- Problems 44 - 48 (p. 416-417)
integrate(asec(x)/(x^2*sqrt(-1+x^2)), x)
 (46)
Type: Union(Expression(Integer),...)
fricas
integrate(acsc(x)/(x^2*(-1+x^2)^(5/2)), x)
 (47)
Type: Union(Expression(Integer),...)
fricas
integrate(acsc(x)^4/(x^2*sqrt(-1+x^2)), x)
 (48)
Type: Union(Expression(Integer),...)
fricas
integrate((-1+x^2)^(3/2)*asec(x)^2/x^5, x)
 (49)
Type: Union(Expression(Integer),...)
fricas
integrate(asec(x)^3*sqrt(-1+x^2)/x^4, x)
 (50)
Type: Union(Expression(Integer),...)
fricas
-- Problems 49 - 56 (p. 422)
integrate(asin(sqrt((-a+x)/(a+x))), x)
 (51)
Type: Union(Expression(Integer),...)
fricas
integrate(atan(sqrt((-a+x)/(a+x))), x)
 (52)
Type: Union(Expression(Integer),...)
fricas
integrate(atan(x)/(1+x)^3, x)
 (53)
Type: Union(Expression(Integer),...)
fricas
integrate(atan(-a+x)/(a+x), x)
 (54)
Type: Union(Expression(Integer),...)
fricas
integrate(asin(sqrt(1-x^2))/sqrt(1-x^2), x)
 (55)
Type: Union(Expression(Integer),...)
fricas
integrate(x*atan(sqrt(1+x^2))/sqrt(1+x^2), x)
 (56)
Type: Union(Expression(Integer),...)
fricas
integrate(asin(x)/(1-x)^(5/2), x)
 (57)
Type: Union(Expression(Integer),...)
fricas
integrate((-1+x)^(5/2)*acsc(x), x)
 (58)
Type: Union(Expression(Integer),...)
fricas
-- Problems 57 - 59 (p. 427)
fricas
)set output tex off

fricas
)set output algebra on
integrate(asin(sinh(x))*sech(x)^4, x)
(59)
6                    5              2             4
4 sinh(x)  + 24 cosh(x)sinh(x)  + (60 cosh(x)  + 12)sinh(x)
+
3                     3
(80 cosh(x)  + 48 cosh(x))sinh(x)
+
4             2             2
(60 cosh(x)  + 72 cosh(x)  + 12)sinh(x)
+
5             3                                 6
(24 cosh(x)  + 48 cosh(x)  + 24 cosh(x))sinh(x) + 4 cosh(x)
+
4             2
12 cosh(x)  + 12 cosh(x)  + 4
*
2                               2
3 sinh(x)  + 6 cosh(x)sinh(x) + 3 cosh(x)  - 1
atan(----------------------------------------------)
+--------------------------------------+
|                2            2
|     - 2 sinh(x)  - 2 cosh(x)  + 6
|--------------------------------------
|       2                             2
\|sinh(x)  - 2 cosh(x)sinh(x) + cosh(x)
+
2                                 2
(- 24 sinh(x)  - 48 cosh(x)sinh(x) - 24 cosh(x)  - 8)
*
2                             2
sinh(x)  + 2 cosh(x)sinh(x) + cosh(x)  - 1
atan(------------------------------------------)
+--------------------------------------+
|                2            2
|     - 2 sinh(x)  - 2 cosh(x)  + 6
|--------------------------------------
|       2                             2
\|sinh(x)  - 2 cosh(x)sinh(x) + cosh(x)
+
4                   3             2            2
sinh(x)  + 4 cosh(x)sinh(x)  + (6 cosh(x)  + 2)sinh(x)
+
3                              4            2
(4 cosh(x)  + 4 cosh(x))sinh(x) + cosh(x)  + 2 cosh(x)  + 1
*
+--------------------------------------+
|                2            2
|     - 2 sinh(x)  - 2 cosh(x)  + 6
|--------------------------------------
|       2                             2
\|sinh(x)  - 2 cosh(x)sinh(x) + cosh(x)
/
6                    5              2             4
6 sinh(x)  + 36 cosh(x)sinh(x)  + (90 cosh(x)  + 18)sinh(x)
+
3                     3
(120 cosh(x)  + 72 cosh(x))sinh(x)
+
4              2             2
(90 cosh(x)  + 108 cosh(x)  + 18)sinh(x)
+
5             3                                 6
(36 cosh(x)  + 72 cosh(x)  + 36 cosh(x))sinh(x) + 6 cosh(x)
+
4             2
18 cosh(x)  + 18 cosh(x)  + 6
Type: Union(Expression(Integer),...)
fricas
integrate(acot(cosh(x))*cosh(x)/sinh(x)^4, x)
(60)
6                   5              2            4
sinh(x)  + 6 cosh(x)sinh(x)  + (15 cosh(x)  - 3)sinh(x)
+
3                     3
(20 cosh(x)  - 12 cosh(x))sinh(x)
+
4             2            2
(15 cosh(x)  - 18 cosh(x)  + 3)sinh(x)
+
5             3                              6            4
(6 cosh(x)  - 12 cosh(x)  + 6 cosh(x))sinh(x) + cosh(x)  - 3 cosh(x)
+
2
3 cosh(x)  - 1
*
log
+-+             2          +-+
(9 \|2  - 12)sinh(x)  + (- 16 \|2  + 24)cosh(x)sinh(x)
+
+-+             2      +-+
(9 \|2  - 12)cosh(x)  + 3 \|2  - 4
/
2          2
sinh(x)  + cosh(x)  + 3
+
+-+       3       +-+              2       +-+       2
- 32 \|2 sinh(x)  - 96 \|2 cosh(x)sinh(x)  - 96 \|2 cosh(x) sinh(x)
+
+-+       3
- 32 \|2 cosh(x)
*
2 sinh(x) + 2 cosh(x)
atan(------------------------------------------)
2                             2
sinh(x)  + 2 cosh(x)sinh(x) + cosh(x)  + 1
+
+-+       4       +-+              3
4 \|2 sinh(x)  + 16 \|2 cosh(x)sinh(x)
+
+-+       2      +-+        2
(24 \|2 cosh(x)  - 8 \|2 )sinh(x)
+
+-+       3       +-+                     +-+       4
(16 \|2 cosh(x)  - 16 \|2 cosh(x))sinh(x) + 4 \|2 cosh(x)
+
+-+       2      +-+
- 8 \|2 cosh(x)  + 4 \|2
/
+-+       6       +-+              5
12 \|2 sinh(x)  + 72 \|2 cosh(x)sinh(x)
+
+-+       2       +-+        4
(180 \|2 cosh(x)  - 36 \|2 )sinh(x)
+
+-+       3        +-+               3
(240 \|2 cosh(x)  - 144 \|2 cosh(x))sinh(x)
+
+-+       4        +-+       2       +-+        2
(180 \|2 cosh(x)  - 216 \|2 cosh(x)  + 36 \|2 )sinh(x)
+
+-+       5        +-+       3       +-+
(72 \|2 cosh(x)  - 144 \|2 cosh(x)  + 72 \|2 cosh(x))sinh(x)
+
+-+       6       +-+       4       +-+       2       +-+
12 \|2 cosh(x)  - 36 \|2 cosh(x)  + 36 \|2 cosh(x)  - 12 \|2
Type: Union(Expression(Integer),...)
fricas
)set output algebra off

fricas
)set output tex on
integrate(%e^x*asin(tanh(x)), x)
 (59)
Type: Union(Expression(Integer),...)