Examples involving exponential function from Albert Rich testsuite.
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-- 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: 0.00 (IN) + 0.01 (EV) + 0.10 (OT) = 0.11 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: 0.00 (EV) + 0.00 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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 (OT) = 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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 (OT) = 0.02 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 (IN) + 0.01 (EV) + 0.01 (OT) = 0.02 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (EV) + 0.00 (OT) = 0.01 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 (EV) + 0 (OT) = 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 0.01 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) = 0.01 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: 0.00 (EV) + 0.00 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (IN) + 0.00 (OT) = 0.00 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: 0.00 (IN) + 0.00 (OT) = 0.00 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 (IN) + 0 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 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 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: 0.00 (EV) + 0.00 (OT) = 0.01 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 (OT) = 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 (OT) = 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: 0.01 (EV) + 0.01 (OT) = 0.01 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 0.01 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 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 (IN) + 0 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.01 (EV) + 0.01 (OT) = 0.02 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 (EV) + 0 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 sec
integrate(%e^(4*x^3)*x^2, x)
3
4 x
%e
(133) ------
12
Type: Union(Expression(Integer),...)
fricas
Time: 0 (IN) + 0 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 0.01 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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 (EV) + 0 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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 (IN) + 0 (OT) = 0 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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 (EV) + 0 (OT) = 0.00 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 (IN) + 0 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.01 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: 0.00 (EV) + 0.00 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 (EV) + 0 (OT) = 0.00 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 (OT) = 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 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 (EV) + 0 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (IN) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 (IN) + 0 (OT) = 0.00 sec
integrate(f^(a+b*x^n), x)
x n
++ b %A + a
(197) | f d%A
++
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 )
(198) --------------------------------
n
Type: Union(Expression(Integer),...)
fricas
Time: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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 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 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.01 (OT) = 0.01 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.00 (EV) + 0.00 (OT) = 0.00 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: 0.01 (EV) + 0.02 (OT) = 0.02 sec
integrate(%e^((-0.1)*x)*x, x)
There are 9 exposed and 11 unexposed library operations named
integrate having 2 argument(s) but none was determined to be
applicable. Use HyperDoc Browse, or issue
)display op integrate
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named
integrate with argument type(s)
Expression(Float)
Variable(x)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
Continuing to read the file...