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Examples involving exponential function from Albert Rich testsuite.

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)set messages time on
 
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)set break resume
 
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)set output algebra on
-- Integrands of the form x^m F^(c (a+b x)^n)
-- n>0 integrate(f^(c*(a+b*x)^2)*x^m, x)
x 2 2 2 ++ m (%A b + 2%A a b + a )c (1) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (IN) + 0.03 (EV) + 0.22 (OT) = 0.28 sec
integrate(f^(c*(a+b*x)^2)*x^3, x)
(2) +------------+ | 2 3 2 2 +---+ (b x + a)\|- b c log(f) (- 2a b c log(f) + 3a b c log(f))\|%pi erf(------------------------) b + 2 2 2 ((2b c x - 2a b c x + 2a c)log(f) - 2) * 2 2 2 +------------+ (b c x + 2a b c x + a c)log(f) | 2 %e \|- b c log(f) / +------------+ 4 2 2 | 2 4b c log(f) \|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(f^(c*(a+b*x)^2)*x^2, x)
(3) +------------+ | 2 2 +---+ (b x + a)\|- b c log(f) (2a b c log(f) - b)\|%pi erf(------------------------) b + 2 2 2 +------------+ (b c x + 2a b c x + a c)log(f) | 2 (2b x - 2a)%e \|- b c log(f) / +------------+ 3 | 2 4b c log(f)\|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(c*(a+b*x)^2)*x, x)
(4) +------------+ | 2 +---+ (b x + a)\|- b c log(f) - a b c log(f)\|%pi erf(------------------------) b + 2 2 2 +------------+ (b c x + 2a b c x + a c)log(f) | 2 %e \|- b c log(f) / +------------+ 2 | 2 2b c log(f)\|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^2), x)
+------------+ | 2 +---+ (b x + a)\|- b c log(f) \|%pi erf(------------------------) b (5) ----------------------------------- +------------+ | 2 2\|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^2)/x, x)
2 2 2 x (%A b + 2%A a b + a )c ++ f (6) | ------------------------ d%A ++ %A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^2)/x^2, x)
2 2 2 x (%A b + 2%A a b + a )c ++ f (7) | ------------------------ d%A ++ 2 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(c*(a+b*x)^2)/x^3, x)
2 2 2 x (%A b + 2%A a b + a )c ++ f (8) | ------------------------ d%A ++ 3 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^3)*x^m, x)
x 3 3 2 2 2 3 ++ m (%A b + 3%A a b + 3%A a b + a )c (9) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^3)*x^2, x)
(10) 3 3 2 2 2 3 +------------+2 (b c x + 3a b c x + 3a b c x + a c)log(f) 3| 3 %e \|- b c log(f) + - 2 1 3 3 2 2 2 3 a b c log(f)Gamma(-,(- b c x - 3a b c x - 3a b c x - a c)log(f)) 3 * +------------+ 3| 3 \|- b c log(f) + 2 2 3 3 2 2 2 3 2a b c log(f)Gamma(-,(- b c x - 3a b c x - 3a b c x - a c)log(f)) 3 / +------------+2 3 3| 3 3b c log(f)\|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^3)*x, x)
(11) +------------+ 1 3 3 2 2 2 3 3| 3 a Gamma(-,(- b c x - 3a b c x - 3a b c x - a c)log(f))\|- b c log(f) 3 + 2 3 3 2 2 2 3 - b Gamma(-,(- b c x - 3a b c x - 3a b c x - a c)log(f)) 3 / +------------+2 3| 3 3b \|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^3), x)
1 3 3 2 2 2 3 Gamma(-,(- b c x - 3a b c x - 3a b c x - a c)log(f)) 3 (12) - ------------------------------------------------------ +------------+ 3| 3 3\|- b c log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^3)/x, x)
3 3 2 2 2 3 x (%A b + 3%A a b + 3%A a b + a )c ++ f (13) | ----------------------------------- d%A ++ %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^3)/x^2, x)
3 3 2 2 2 3 x (%A b + 3%A a b + 3%A a b + a )c ++ f (14) | ----------------------------------- d%A ++ 2 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^3)/x^3, x)
3 3 2 2 2 3 x (%A b + 3%A a b + 3%A a b + a )c ++ f (15) | ----------------------------------- d%A ++ 3 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^m, x)
x 3 3 2 2 2 3 ++ %A b + 3%A a b + 3%A a b + a m (16) | %e %A d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^4, x)
(17) 3 3 2 2 2 3 +----+2 2 2 2 b x + 3a b x + 3a b x + a 3| 3 (3b x - 6a b x + 9a )%e \|- b + +----+ 4 1 3 3 2 2 2 3 3| 3 (- 3a - 4a)b Gamma(-,- b x - 3a b x - 3a b x - a )\|- b 3 + 3 2 2 3 3 2 2 2 3 (12a + 2)b Gamma(-,- b x - 3a b x - 3a b x - a ) 3 / +----+2 5 3| 3 9b \|- b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^3, x)
(18) 3 3 2 2 2 3 +----+2 b x + 3a b x + 3a b x + a 3| 3 (3b x - 6a)%e \|- b + +----+ 3 1 3 3 2 2 2 3 3| 3 (3a + 1)b Gamma(-,- b x - 3a b x - 3a b x - a )\|- b 3 + 2 2 2 3 3 2 2 2 3 - 9a b Gamma(-,- b x - 3a b x - 3a b x - a ) 3 / +----+2 4 3| 3 9b \|- b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^2, x)
(19) 3 3 2 2 2 3 +----+2 b x + 3a b x + 3a b x + a 3| 3 %e \|- b + +----+ 2 1 3 3 2 2 2 3 3| 3 - a b Gamma(-,- b x - 3a b x - 3a b x - a )\|- b 3 + 2 2 3 3 2 2 2 3 2a b Gamma(-,- b x - 3a b x - 3a b x - a ) 3 / +----+2 3 3| 3 3b \|- b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x, x)
(20) +----+ 1 3 3 2 2 2 3 3| 3 a Gamma(-,- b x - 3a b x - 3a b x - a )\|- b 3 + 2 3 3 2 2 2 3 - b Gamma(-,- b x - 3a b x - 3a b x - a ) 3 / +----+2 3| 3 3b \|- b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3), x)
1 3 3 2 2 2 3 Gamma(-,- b x - 3a b x - 3a b x - a ) 3 (21) - --------------------------------------- +----+ 3| 3 3\|- b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)/x, x)
3 3 2 2 2 3 x %A b + 3%A a b + 3%A a b + a ++ %e (22) | --------------------------------- d%A ++ %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(%e^sqrt(5+3*x), x)
+------+ +------+ \|3x + 5 (2\|3x + 5 - 2)%e (23) --------------------------- 3
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- n<0 integrate(f^(c/(a+b*x))*x^m, x)
c x -------- ++ m %A b + a (24) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.01 (EV) = 0.02 sec
integrate(f^(c/(a+b*x))*x^4, x)
(25) 4 4 4 2 3 2 3 2 3 3 (b c x + a c )log(f) + (b c x - 18a b c x - 19a c )log(f) + 3 2 3 2 2 2 2 2 3 2 2 (2b c x - 14a b c x + 86a b c x + 102a c )log(f) + 4 4 3 3 2 2 2 3 4 (6b c x - 16a b c x + 36a b c x - 96a b c x - 154a c)log(f) + 5 5 5 24b x + 24a * c log(f) -------- b x + a %e + 5 5 4 4 2 3 3 3 2 2 - c log(f) + 20a c log(f) - 120a c log(f) + 240a c log(f) + 4 - 120a c log(f) * c log(f) Ei(--------) b x + a / 5 120b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x))*x^3, x)
(26) 3 3 3 2 2 2 2 2 2 2 (b c x + a c )log(f) + (b c x - 10a b c x - 11a c )log(f) + 3 3 2 2 2 3 4 4 4 (2b c x - 6a b c x + 18a b c x + 26a c)log(f) + 6b x - 6a * c log(f) -------- b x + a %e + 4 4 3 3 2 2 2 3 c log(f) (- c log(f) + 12a c log(f) - 36a c log(f) + 24a c log(f))Ei(--------) b x + a / 4 24b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(c/(a+b*x))*x^2, x)
(27) 2 2 2 2 2 2 3 3 (b c x + a c )log(f) + (b c x - 4a b c x - 5a c)log(f) + 2b x + 3 2a * c log(f) -------- b x + a %e + 3 3 2 2 2 c log(f) (- c log(f) + 6a c log(f) - 6a c log(f))Ei(--------) b x + a / 3 6b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x))*x, x)
(28) c log(f) -------- 2 2 2 b x + a ((b c x + a c)log(f) + b x - a )%e + 2 2 c log(f) (- c log(f) + 2a c log(f))Ei(--------) b x + a / 2 2b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)), x)
c log(f) -------- b x + a c log(f) (b x + a)%e - c log(f)Ei(--------) b x + a (29) ------------------------------------------ b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x))/x, x)
c log(f) -------- b c x log(f) a c log(f) (30) Ei(- ------------)%e - Ei(--------) 2 b x + a a b x + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(c/(a+b*x))/x^2, x)
c log(f) c log(f) -------- -------- b c x log(f) a 2 b x + a - b c x log(f)Ei(- ------------)%e + (- a b x - a )%e 2 a b x + a (31) --------------------------------------------------------------------- 2 a x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(c/(a+b*x))/x^3, x)
(32) c log(f) -------- 2 2 2 2 2 2 b c x log(f) a (b c x log(f) + 2a b c x log(f))Ei(- ------------)%e 2 a b x + a + c log(f) -------- 2 2 2 2 2 2 4 b x + a ((a b c x + a b c x)log(f) + a b x - a )%e / 4 2 2a x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x)^2)*x^m, x)
c -------------------- x 2 2 2 ++ m %A b + 2%A a b + a (33) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(f^(c/(a+b*x)^2)*x^4, x)
(34) +----------+ | c log(f) b |- -------- | 2 3 3 2 2 2 4 +---+ \| b (- 4c log(f) - 60a c log(f) - 15a c log(f))\|%pi erf(--------------) b x + a + 2 2 2 2 (4b c x + 4a b c )log(f) + 4 3 3 2 2 2 3 6 5 5 (2b c x - 9a b c x + 36a b c x + 47a b c)log(f) + 3b x + 3a b * c log(f) ------------------ 2 2 2 b x + 2a b x + a %e + 2 2 3 c log(f) (15a b c log(f) + 30a b c log(f))Ei(------------------) 2 2 2 b x + 2a b x + a * +----------+ | c log(f) |- -------- | 2 \| b / +----------+ 6 | c log(f) 15b |- -------- | 2 \| b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^2)*x^3, x)
(35) +----------+ | c log(f) b |- -------- | 2 2 2 3 +---+ \| b (8a c log(f) + 4a c log(f))\|%pi erf(--------------) b x + a + c log(f) ------------------ 2 2 2 3 2 2 2 5 4 4 b x + 2a b x + a ((b c x - 6a b c x - 7a b c)log(f) + b x - a b)%e + 2 2 2 c log(f) (- b c log(f) - 6a b c log(f))Ei(------------------) 2 2 2 b x + 2a b x + a * +----------+ | c log(f) |- -------- | 2 \| b / +----------+ 5 | c log(f) 4b |- -------- | 2 \| b
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(f^(c/(a+b*x)^2)*x^2, x)
(36) +----------+ | c log(f) b |- -------- | 2 2 2 2 +---+ \| b (- 2c log(f) - 3a c log(f))\|%pi erf(--------------) b x + a + c log(f) ------------------ 2 2 2 2 4 3 3 b x + 2a b x + a ((2b c x + 2a b c)log(f) + b x + a b)%e + c log(f) 3a b c log(f)Ei(------------------) 2 2 2 b x + 2a b x + a * +----------+ | c log(f) |- -------- | 2 \| b / +----------+ 4 | c log(f) 3b |- -------- | 2 \| b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^2)*x, x)
(37) +----------+ | c log(f) b |- -------- | 2 +---+ \| b 2a c log(f)\|%pi erf(--------------) b x + a + c log(f) ------------------ 2 2 2 3 2 2 b x + 2a b x + a c log(f) ((b x - a b)%e - b c log(f)Ei(------------------)) 2 2 2 b x + 2a b x + a * +----------+ | c log(f) |- -------- | 2 \| b / +----------+ 3 | c log(f) 2b |- -------- | 2 \| b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^2), x)
(38) +----------+ | c log(f) b |- -------- | 2 +---+ \| b - c log(f)\|%pi erf(--------------) b x + a + c log(f) ------------------ 2 2 2 +----------+ 2 b x + 2a b x + a | c log(f) (b x + a b)%e |- -------- | 2 \| b / +----------+ 2 | c log(f) b |- -------- | 2 \| b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x)^2)/x, x)
c -------------------- 2 2 2 x %A b + 2%A a b + a ++ f (39) | --------------------- d%A ++ %A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c/(a+b*x)^2)/x^2, x)
c -------------------- 2 2 2 x %A b + 2%A a b + a ++ f (40) | --------------------- d%A ++ 2 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^2)/x^3, x)
c -------------------- 2 2 2 x %A b + 2%A a b + a ++ f (41) | --------------------- d%A ++ 3 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^3)*x^m, x)
c ------------------------------- x 3 3 2 2 2 3 ++ m %A b + 3%A a b + 3%A a b + a (42) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(f^(c/(a+b*x)^3)*x^4, x)
(43) 4 2 3 2 2 7 5 5 2 ((3b c x - 24a b c x - 27a b c)log(f) + 2b x + 2a b ) * c log(f) ---------------------------- 3 3 2 2 2 3 b x + 3a b x + 3a b x + a %e + 2 2 c log(f) - 20a b c log(f)Ei(----------------------------) 3 3 2 2 2 3 b x + 3a b x + 3a b x + a * +----------+2 | c log(f) |- -------- 3| 3 \| b + 2 2 3 1 c log(f) (3b c log(f) - 20a b c log(f))Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 b x + 3a b x + 3a b x + a * +----------+ | c log(f) |- -------- 3| 3 \| b + 2 2 4 2 c log(f) (- 30a c log(f) + 10a c log(f))Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 b x + 3a b x + 3a b x + a / +----------+2 7 | c log(f) 10b |- -------- 3| 3 \| b
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(f^(c/(a+b*x)^3)*x^3, x)
(44) c log(f) ---------------------------- 3 3 2 2 2 3 3 2 6 4 4 2 b x + 3a b x + 3a b x + a ((3b c x + 3a b c)log(f) + b x - a b )%e + 2 c log(f) 4a b c log(f)Ei(----------------------------) 3 3 2 2 2 3 b x + 3a b x + 3a b x + a * +----------+2 | c log(f) |- -------- 3| 3 \| b + +----------+ 2 1 c log(f) | c log(f) 6a b c log(f)Gamma(-,- ----------------------------) |- -------- 3 3 3 2 2 2 3 3| 3 b x + 3a b x + 3a b x + a \| b + 2 2 3 2 c log(f) (3c log(f) - 4a c log(f))Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 b x + 3a b x + 3a b x + a / +----------+2 6 | c log(f) 4b |- -------- 3| 3 \| b
Type: Union(Expression(Integer),...)
fricas
Time: 0.06 (EV) = 0.06 sec
integrate(f^(c/(a+b*x)^3)*x^2, x)
(45) c log(f) ---------------------------- 3 3 2 2 2 3 5 3 3 2 b x + 3a b x + 3a b x + a (b x + a b )%e + 2 c log(f) - b c log(f)Ei(----------------------------) 3 3 2 2 2 3 b x + 3a b x + 3a b x + a * +----------+2 | c log(f) |- -------- 3| 3 \| b + +----------+ 1 c log(f) | c log(f) - 3a b c log(f)Gamma(-,- ----------------------------) |- -------- 3 3 3 2 2 2 3 3| 3 b x + 3a b x + 3a b x + a \| b + 2 2 c log(f) 3a c log(f)Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 b x + 3a b x + 3a b x + a / +----------+2 5 | c log(f) 3b |- -------- 3| 3 \| b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^3)*x, x)
(46) c log(f) ---------------------------- 3 3 2 2 2 3 +----------+2 4 2 2 2 b x + 3a b x + 3a b x + a | c log(f) (b x - a b )%e |- -------- 3| 3 \| b + +----------+ 1 c log(f) | c log(f) b c log(f)Gamma(-,- ----------------------------) |- -------- 3 3 3 2 2 2 3 3| 3 b x + 3a b x + 3a b x + a \| b + 2 c log(f) - 2a c log(f)Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 b x + 3a b x + 3a b x + a / +----------+2 4 | c log(f) 2b |- -------- 3| 3 \| b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^3), x)
(47) c log(f) ---------------------------- 3 3 2 2 2 3 +----------+2 3 2 b x + 3a b x + 3a b x + a | c log(f) (b x + a b )%e |- -------- 3| 3 \| b + 2 c log(f) c log(f)Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 b x + 3a b x + 3a b x + a / +----------+2 3 | c log(f) b |- -------- 3| 3 \| b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^3)/x, x)
c ------------------------------- 3 3 2 2 2 3 x %A b + 3%A a b + 3%A a b + a ++ f (48) | -------------------------------- d%A ++ %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^3)/x^2, x)
c ------------------------------- 3 3 2 2 2 3 x %A b + 3%A a b + 3%A a b + a ++ f (49) | -------------------------------- d%A ++ 2 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c/(a+b*x)^3)/x^3, x)
c ------------------------------- 3 3 2 2 2 3 x %A b + 3%A a b + 3%A a b + a ++ f (50) | -------------------------------- d%A ++ 3 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
-- n symbolic integrate(f^(c*(a+b*x)^n)*x^m, x)
x n ++ m c (%A b + a) (51) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(c*(a+b*x)^n)*x^3, x)
x n ++ 3 c (%A b + a) (52) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^n)*x^2, x)
x n ++ 2 c (%A b + a) (53) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^n)*x, x)
x n ++ c (%A b + a) (54) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^n), x)
x n ++ c (%A b + a) (55) | f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^n)/x, x)
n x c (%A b + a) ++ f (56) | -------------- d%A ++ %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(c*(a+b*x)^n)/x^2, x)
n x c (%A b + a) ++ f (57) | -------------- d%A ++ 2 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(c*(a+b*x)^n)/x^3, x)
n x c (%A b + a) ++ f (58) | -------------- d%A ++ 3 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
-- Integrands of the form (c+d x)^m F^(a+b (c+d x)^n)
-- n>0 integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^m, x)
x 2 2 2 ++ %A b d + 2%A b c d + b c + a m (59) | F (%A d + c) d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^11, x)
(60) 5 10 10 5 9 9 5 2 8 8 5 3 7 7 5 4 6 6 b d x + 10b c d x + 45b c d x + 120b c d x + 210b c d x + 5 5 5 5 5 6 4 4 5 7 3 3 5 8 2 2 5 9 252b c d x + 210b c d x + 120b c d x + 45b c d x + 10b c d x + 5 10 b c * 5 log(F) + 4 8 8 4 7 7 4 2 6 6 4 3 5 5 4 4 4 4 - 5b d x - 40b c d x - 140b c d x - 280b c d x - 350b c d x + 4 5 3 3 4 6 2 2 4 7 4 8 - 280b c d x - 140b c d x - 40b c d x - 5b c * 4 log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 20b d x + 120b c d x + 300b c d x + 400b c d x + 300b c d x + 3 5 3 6 120b c d x + 20b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 60b d x - 240b c d x - 360b c d x - 240b c d x - 60b c )log(F) + 2 2 2 (120b d x + 240b c d x + 120b c )log(F) - 120 * 2 2 2 (b d x + 2b c d x + b c + a)log(F) %e / 6 6 2b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^9, x)
(61) 4 8 8 4 7 7 4 2 6 6 4 3 5 5 4 4 4 4 b d x + 8b c d x + 28b c d x + 56b c d x + 70b c d x + 4 5 3 3 4 6 2 2 4 7 4 8 56b c d x + 28b c d x + 8b c d x + b c * 4 log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 - 4b d x - 24b c d x - 60b c d x - 80b c d x - 60b c d x + 3 5 3 6 - 24b c d x - 4b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (12b d x + 48b c d x + 72b c d x + 48b c d x + 12b c )log(F) + 2 2 2 (- 24b d x - 48b c d x - 24b c )log(F) + 24 * 2 2 2 (b d x + 2b c d x + b c + a)log(F) %e / 5 5 2b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^7, x)
(62) 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 b d x + 6b c d x + 15b c d x + 20b c d x + 15b c d x + 3 5 3 6 6b c d x + b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 3b d x - 12b c d x - 18b c d x - 12b c d x - 3b c )log(F) + 2 2 2 (6b d x + 12b c d x + 6b c )log(F) - 6 * 2 2 2 (b d x + 2b c d x + b c + a)log(F) %e / 4 4 2b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^5, x)
(63) 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (b d x + 4b c d x + 6b c d x + 4b c d x + b c )log(F) + 2 2 2 (- 2b d x - 4b c d x - 2b c )log(F) + 2 * 2 2 2 (b d x + 2b c d x + b c + a)log(F) %e / 3 3 2b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^3, x)
(64) 2 2 2 2 2 2 (b d x + 2b c d x + b c + a)log(F) ((b d x + 2b c d x + b c )log(F) - 1)%e ---------------------------------------------------------------------------- 2 2 2b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x), x)
2 2 2 (b d x + 2b c d x + b c + a)log(F) %e (65) -------------------------------------- 2b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x), x)
2 2 2 a log(F) Ei((b d x + 2b c d x + b c )log(F))%e (66) ---------------------------------------------- 2d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^3, x)
(67) 2 2 2 (b d x + 2b c d x + b c + a)log(F) - %e + 2 2 2 2 2 2 (b d x + 2b c d x + b c )log(F)Ei((b d x + 2b c d x + b c )log(F)) * a log(F) %e / 3 2 2 2 2d x + 4c d x + 2c d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^5, x)
(68) 2 2 2 ((- b d x - 2b c d x - b c )log(F) - 1) * 2 2 2 (b d x + 2b c d x + b c + a)log(F) %e + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (b d x + 4b c d x + 6b c d x + 4b c d x + b c )log(F) * 2 2 2 a log(F) Ei((b d x + 2b c d x + b c )log(F))%e / 5 4 4 3 2 3 2 3 2 4 4d x + 16c d x + 24c d x + 16c d x + 4c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^7, x)
(69) 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- b d x - 4b c d x - 6b c d x - 4b c d x - b c )log(F) + 2 2 2 (- b d x - 2b c d x - b c )log(F) - 2 * 2 2 2 (b d x + 2b c d x + b c + a)log(F) %e + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 3 5 b d x + 6b c d x + 15b c d x + 20b c d x + 15b c d x + 6b c d x + 3 6 b c * 3 2 2 2 a log(F) log(F) Ei((b d x + 2b c d x + b c )log(F))%e / 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 6 12d x + 72c d x + 180c d x + 240c d x + 180c d x + 72c d x + 12c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^9, x)
(70) 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 - b d x - 6b c d x - 15b c d x - 20b c d x - 15b c d x + 3 5 3 6 - 6b c d x - b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- b d x - 4b c d x - 6b c d x - 4b c d x - b c )log(F) + 2 2 2 (- 2b d x - 4b c d x - 2b c )log(F) - 6 * 2 2 2 (b d x + 2b c d x + b c + a)log(F) %e + 4 8 8 4 7 7 4 2 6 6 4 3 5 5 4 4 4 4 b d x + 8b c d x + 28b c d x + 56b c d x + 70b c d x + 4 5 3 3 4 6 2 2 4 7 4 8 56b c d x + 28b c d x + 8b c d x + b c * 4 2 2 2 a log(F) log(F) Ei((b d x + 2b c d x + b c )log(F))%e / 9 8 8 7 2 7 6 3 6 5 4 5 4 5 4 3 48d x + 384c d x + 1344c d x + 2688c d x + 3360c d x + 2688c d x + 6 3 2 7 2 8 1344c d x + 384c d x + 48c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^11, x)
(71) 4 8 8 4 7 7 4 2 6 6 4 3 5 5 4 4 4 4 - b d x - 8b c d x - 28b c d x - 56b c d x - 70b c d x + 4 5 3 3 4 6 2 2 4 7 4 8 - 56b c d x - 28b c d x - 8b c d x - b c * 4 log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 - b d x - 6b c d x - 15b c d x - 20b c d x - 15b c d x + 3 5 3 6 - 6b c d x - b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 2b d x - 8b c d x - 12b c d x - 8b c d x - 2b c )log(F) + 2 2 2 (- 6b d x - 12b c d x - 6b c )log(F) - 24 * 2 2 2 (b d x + 2b c d x + b c + a)log(F) %e + 5 10 10 5 9 9 5 2 8 8 5 3 7 7 5 4 6 6 b d x + 10b c d x + 45b c d x + 120b c d x + 210b c d x + 5 5 5 5 5 6 4 4 5 7 3 3 5 8 2 2 5 9 252b c d x + 210b c d x + 120b c d x + 45b c d x + 10b c d x + 5 10 b c * 5 2 2 2 a log(F) log(F) Ei((b d x + 2b c d x + b c )log(F))%e / 11 10 10 9 2 9 8 3 8 7 4 7 6 240d x + 2400c d x + 10800c d x + 28800c d x + 50400c d x + 5 6 5 6 5 4 7 4 3 8 3 2 9 2 10 60480c d x + 50400c d x + 28800c d x + 10800c d x + 2400c d x + 240c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^12, x)
(72) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) 10395d\|%pi %e erf(------------------------) d + 5 11 11 5 10 10 5 2 9 9 5 3 8 8 64b d x + 704b c d x + 3520b c d x + 10560b c d x + 5 4 7 7 5 5 6 6 5 6 5 5 5 7 4 4 21120b c d x + 29568b c d x + 29568b c d x + 21120b c d x + 5 8 3 3 5 9 2 2 5 10 5 11 10560b c d x + 3520b c d x + 704b c d x + 64b c * 5 log(F) + 4 9 9 4 8 8 4 2 7 7 4 3 6 6 - 352b d x - 3168b c d x - 12672b c d x - 29568b c d x + 4 4 5 5 4 5 4 4 4 6 3 3 4 7 2 2 - 44352b c d x - 44352b c d x - 29568b c d x - 12672b c d x + 4 8 4 9 - 3168b c d x - 352b c * 4 log(F) + 3 7 7 3 6 6 3 2 5 5 3 3 4 4 1584b d x + 11088b c d x + 33264b c d x + 55440b c d x + 3 4 3 3 3 5 2 2 3 6 3 7 55440b c d x + 33264b c d x + 11088b c d x + 1584b c * 3 log(F) + 2 5 5 2 4 4 2 2 3 3 2 3 2 2 - 5544b d x - 27720b c d x - 55440b c d x - 55440b c d x + 2 4 2 5 - 27720b c d x - 5544b c * 2 log(F) + 3 3 2 2 2 3 (13860b d x + 41580b c d x + 41580b c d x + 13860b c )log(F) + - 20790d x - 20790c * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 6 6 | 2 128b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^10, x)
(73) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) - 945d\|%pi %e erf(------------------------) d + 4 9 9 4 8 8 4 2 7 7 4 3 6 6 32b d x + 288b c d x + 1152b c d x + 2688b c d x + 4 4 5 5 4 5 4 4 4 6 3 3 4 7 2 2 4032b c d x + 4032b c d x + 2688b c d x + 1152b c d x + 4 8 4 9 288b c d x + 32b c * 4 log(F) + 3 7 7 3 6 6 3 2 5 5 3 3 4 4 - 144b d x - 1008b c d x - 3024b c d x - 5040b c d x + 3 4 3 3 3 5 2 2 3 6 3 7 - 5040b c d x - 3024b c d x - 1008b c d x - 144b c * 3 log(F) + 2 5 5 2 4 4 2 2 3 3 2 3 2 2 504b d x + 2520b c d x + 5040b c d x + 5040b c d x + 2 4 2 5 2520b c d x + 504b c * 2 log(F) + 3 3 2 2 2 3 (- 1260b d x - 3780b c d x - 3780b c d x - 1260b c )log(F) + 1890d x + 1890c * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 5 5 | 2 64b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^8, x)
(74) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) 105d\|%pi %e erf(------------------------) d + 3 7 7 3 6 6 3 2 5 5 3 3 4 4 3 4 3 3 16b d x + 112b c d x + 336b c d x + 560b c d x + 560b c d x + 3 5 2 2 3 6 3 7 336b c d x + 112b c d x + 16b c * 3 log(F) + 2 5 5 2 4 4 2 2 3 3 2 3 2 2 2 4 - 56b d x - 280b c d x - 560b c d x - 560b c d x - 280b c d x + 2 5 - 56b c * 2 log(F) + 3 3 2 2 2 3 (140b d x + 420b c d x + 420b c d x + 140b c )log(F) - 210d x - 210c * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 4 4 | 2 32b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^6, x)
(75) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) - 15d\|%pi %e erf(------------------------) d + 2 5 5 2 4 4 2 2 3 3 2 3 2 2 2 4 8b d x + 40b c d x + 80b c d x + 80b c d x + 40b c d x + 2 5 8b c * 2 log(F) + 3 3 2 2 2 3 (- 20b d x - 60b c d x - 60b c d x - 20b c )log(F) + 30d x + 30c * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 3 3 | 2 16b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^4, x)
(76) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) 3d\|%pi %e erf(------------------------) d + 3 3 2 2 2 3 ((4b d x + 12b c d x + 12b c d x + 4b c )log(F) - 6d x - 6c) * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 2 2 | 2 8b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^2, x)
(77) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) - d\|%pi %e erf(------------------------) d + 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 (2d x + 2c)%e \|- b d log(F) / +------------+ | 2 4b d log(F)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2), x)
+------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) \|%pi %e erf(------------------------) d (78) --------------------------------------------- +------------+ | 2 2\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^2, x)
(79) +------------+ | 2 2 +---+ a log(F) (d x + c)\|- b d log(F) (b d x + b c d)log(F)\|%pi %e erf(------------------------) d + 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 - %e \|- b d log(F) / +------------+ 2 | 2 (d x + c d)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^4, x)
(80) 2 4 3 2 3 2 2 2 2 2 3 2 +---+ a log(F) (2b d x + 6b c d x + 6b c d x + 2b c d)log(F) \|%pi %e * +------------+ | 2 (d x + c)\|- b d log(F) erf(------------------------) d + 2 2 2 ((- 2b d x - 4b c d x - 2b c )log(F) - 1) * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 4 3 3 2 2 2 3 | 2 (3d x + 9c d x + 9c d x + 3c d)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^6, x)
(81) 3 6 5 3 5 4 3 2 4 3 3 3 3 2 3 4 2 3 5 (4b d x + 20b c d x + 40b c d x + 40b c d x + 20b c d x + 4b c d) * +------------+ | 2 3 +---+ a log(F) (d x + c)\|- b d log(F) log(F) \|%pi %e erf(------------------------) d + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 4b d x - 16b c d x - 24b c d x - 16b c d x - 4b c )log(F) + 2 2 2 (- 2b d x - 4b c d x - 2b c )log(F) - 3 * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / 6 5 5 4 2 4 3 3 3 2 4 2 5 (15d x + 75c d x + 150c d x + 150c d x + 75c d x + 15c d) * +------------+ | 2 \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^8, x)
(82) 4 8 7 4 7 6 4 2 6 5 4 3 5 4 4 4 4 3 8b d x + 56b c d x + 168b c d x + 280b c d x + 280b c d x + 4 5 3 2 4 6 2 4 7 168b c d x + 56b c d x + 8b c d * +------------+ | 2 4 +---+ a log(F) (d x + c)\|- b d log(F) log(F) \|%pi %e erf(------------------------) d + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 - 8b d x - 48b c d x - 120b c d x - 160b c d x - 120b c d x + 3 5 3 6 - 48b c d x - 8b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 4b d x - 16b c d x - 24b c d x - 16b c d x - 4b c )log(F) + 2 2 2 (- 6b d x - 12b c d x - 6b c )log(F) - 15 * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / 8 7 7 6 2 6 5 3 5 4 4 4 3 5 3 2 105d x + 735c d x + 2205c d x + 3675c d x + 3675c d x + 2205c d x + 6 2 7 735c d x + 105c d * +------------+ | 2 \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^10, x)
(83) 5 10 9 5 9 8 5 2 8 7 5 3 7 6 5 4 6 5 16b d x + 144b c d x + 576b c d x + 1344b c d x + 2016b c d x + 5 5 5 4 5 6 4 3 5 7 3 2 5 8 2 5 9 2016b c d x + 1344b c d x + 576b c d x + 144b c d x + 16b c d * +------------+ | 2 5 +---+ a log(F) (d x + c)\|- b d log(F) log(F) \|%pi %e erf(------------------------) d + 4 8 8 4 7 7 4 2 6 6 4 3 5 5 - 16b d x - 128b c d x - 448b c d x - 896b c d x + 4 4 4 4 4 5 3 3 4 6 2 2 4 7 4 8 - 1120b c d x - 896b c d x - 448b c d x - 128b c d x - 16b c * 4 log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 - 8b d x - 48b c d x - 120b c d x - 160b c d x - 120b c d x + 3 5 3 6 - 48b c d x - 8b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 12b d x - 48b c d x - 72b c d x - 48b c d x - 12b c )log(F) + 2 2 2 (- 30b d x - 60b c d x - 30b c )log(F) - 105 * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / 10 9 9 8 2 8 7 3 7 6 4 6 5 945d x + 8505c d x + 34020c d x + 79380c d x + 119070c d x + 5 5 4 6 4 3 7 3 2 8 2 9 119070c d x + 79380c d x + 34020c d x + 8505c d x + 945c d * +------------+ | 2 \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^12, x)
(84) 6 12 11 6 11 10 6 2 10 9 6 3 9 8 32b d x + 352b c d x + 1760b c d x + 5280b c d x + 6 4 8 7 6 5 7 6 6 6 6 5 6 7 5 4 10560b c d x + 14784b c d x + 14784b c d x + 10560b c d x + 6 8 4 3 6 9 3 2 6 10 2 6 11 5280b c d x + 1760b c d x + 352b c d x + 32b c d * +------------+ | 2 6 +---+ a log(F) (d x + c)\|- b d log(F) log(F) \|%pi %e erf(------------------------) d + 5 10 10 5 9 9 5 2 8 8 5 3 7 7 - 32b d x - 320b c d x - 1440b c d x - 3840b c d x + 5 4 6 6 5 5 5 5 5 6 4 4 5 7 3 3 - 6720b c d x - 8064b c d x - 6720b c d x - 3840b c d x + 5 8 2 2 5 9 5 10 - 1440b c d x - 320b c d x - 32b c * 5 log(F) + 4 8 8 4 7 7 4 2 6 6 4 3 5 5 - 16b d x - 128b c d x - 448b c d x - 896b c d x + 4 4 4 4 4 5 3 3 4 6 2 2 4 7 4 8 - 1120b c d x - 896b c d x - 448b c d x - 128b c d x - 16b c * 4 log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 - 24b d x - 144b c d x - 360b c d x - 480b c d x + 3 4 2 2 3 5 3 6 - 360b c d x - 144b c d x - 24b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 60b d x - 240b c d x - 360b c d x - 240b c d x - 60b c )log(F) + 2 2 2 (- 210b d x - 420b c d x - 210b c )log(F) - 945 * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / 12 11 11 10 2 10 9 3 9 8 10395d x + 114345c d x + 571725c d x + 1715175c d x + 4 8 7 5 7 6 6 6 5 7 5 4 3430350c d x + 4802490c d x + 4802490c d x + 3430350c d x + 8 4 3 9 3 2 10 2 11 1715175c d x + 571725c d x + 114345c d x + 10395c d * +------------+ | 2 \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^m, x)
x 3 3 2 2 2 3 ++ %A b d + 3%A b c d + 3%A b c d + b c + a m (85) | F (%A d + c) d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.01 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^17, x)
(86) 5 15 15 5 14 14 5 2 13 13 5 3 12 12 b d x + 15b c d x + 105b c d x + 455b c d x + 5 4 11 11 5 5 10 10 5 6 9 9 5 7 8 8 1365b c d x + 3003b c d x + 5005b c d x + 6435b c d x + 5 8 7 7 5 9 6 6 5 10 5 5 5 11 4 4 6435b c d x + 5005b c d x + 3003b c d x + 1365b c d x + 5 12 3 3 5 13 2 2 5 14 5 15 455b c d x + 105b c d x + 15b c d x + b c * 5 log(F) + 4 12 12 4 11 11 4 2 10 10 4 3 9 9 - 5b d x - 60b c d x - 330b c d x - 1100b c d x + 4 4 8 8 4 5 7 7 4 6 6 6 4 7 5 5 - 2475b c d x - 3960b c d x - 4620b c d x - 3960b c d x + 4 8 4 4 4 9 3 3 4 10 2 2 4 11 4 12 - 2475b c d x - 1100b c d x - 330b c d x - 60b c d x - 5b c * 4 log(F) + 3 9 9 3 8 8 3 2 7 7 3 3 6 6 3 4 5 5 20b d x + 180b c d x + 720b c d x + 1680b c d x + 2520b c d x + 3 5 4 4 3 6 3 3 3 7 2 2 3 8 3 9 2520b c d x + 1680b c d x + 720b c d x + 180b c d x + 20b c * 3 log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 - 60b d x - 360b c d x - 900b c d x - 1200b c d x - 900b c d x + 2 5 2 6 - 360b c d x - 60b c * 2 log(F) + 3 3 2 2 2 3 (120b d x + 360b c d x + 360b c d x + 120b c )log(F) - 120 * 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) %e / 6 6 3b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^14, x)
(87) 4 12 12 4 11 11 4 2 10 10 4 3 9 9 4 4 8 8 b d x + 12b c d x + 66b c d x + 220b c d x + 495b c d x + 4 5 7 7 4 6 6 6 4 7 5 5 4 8 4 4 4 9 3 3 792b c d x + 924b c d x + 792b c d x + 495b c d x + 220b c d x + 4 10 2 2 4 11 4 12 66b c d x + 12b c d x + b c * 4 log(F) + 3 9 9 3 8 8 3 2 7 7 3 3 6 6 3 4 5 5 - 4b d x - 36b c d x - 144b c d x - 336b c d x - 504b c d x + 3 5 4 4 3 6 3 3 3 7 2 2 3 8 3 9 - 504b c d x - 336b c d x - 144b c d x - 36b c d x - 4b c * 3 log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 12b d x + 72b c d x + 180b c d x + 240b c d x + 180b c d x + 2 5 2 6 72b c d x + 12b c * 2 log(F) + 3 3 2 2 2 3 (- 24b d x - 72b c d x - 72b c d x - 24b c )log(F) + 24 * 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) %e / 5 5 3b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^11, x)
(88) 3 9 9 3 8 8 3 2 7 7 3 3 6 6 3 4 5 5 b d x + 9b c d x + 36b c d x + 84b c d x + 126b c d x + 3 5 4 4 3 6 3 3 3 7 2 2 3 8 3 9 126b c d x + 84b c d x + 36b c d x + 9b c d x + b c * 3 log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 - 3b d x - 18b c d x - 45b c d x - 60b c d x - 45b c d x + 2 5 2 6 - 18b c d x - 3b c * 2 log(F) + 3 3 2 2 2 3 (6b d x + 18b c d x + 18b c d x + 6b c )log(F) - 6 * 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) %e / 4 4 3b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^8, x)
(89) 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 b d x + 6b c d x + 15b c d x + 20b c d x + 15b c d x + 2 5 2 6 6b c d x + b c * 2 log(F) + 3 3 2 2 2 3 (- 2b d x - 6b c d x - 6b c d x - 2b c )log(F) + 2 * 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) %e / 3 3 3b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^5, x)
(90) 3 3 2 2 2 3 ((b d x + 3b c d x + 3b c d x + b c )log(F) - 1) * 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) %e / 2 2 3b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^2, x)
3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) %e (91) -------------------------------------------------- 3b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x), x)
3 3 2 2 2 3 a log(F) Ei((b d x + 3b c d x + 3b c d x + b c )log(F))%e (92) ---------------------------------------------------------- 3d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^4, x)
(93) 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) - %e + 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c )log(F) * 3 3 2 2 2 3 a log(F) Ei((b d x + 3b c d x + 3b c d x + b c )log(F))%e / 4 3 3 2 2 2 3 3d x + 9c d x + 9c d x + 3c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^7, x)
(94) 3 3 2 2 2 3 ((- b d x - 3b c d x - 3b c d x - b c )log(F) - 1) * 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) %e + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 2 5 b d x + 6b c d x + 15b c d x + 20b c d x + 15b c d x + 6b c d x + 2 6 b c * 2 3 3 2 2 2 3 a log(F) log(F) Ei((b d x + 3b c d x + 3b c d x + b c )log(F))%e / 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 6 6d x + 36c d x + 90c d x + 120c d x + 90c d x + 36c d x + 6c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^10, x)
(95) 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 - b d x - 6b c d x - 15b c d x - 20b c d x - 15b c d x + 2 5 2 6 - 6b c d x - b c * 2 log(F) + 3 3 2 2 2 3 (- b d x - 3b c d x - 3b c d x - b c )log(F) - 2 * 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) %e + 3 9 9 3 8 8 3 2 7 7 3 3 6 6 3 4 5 5 b d x + 9b c d x + 36b c d x + 84b c d x + 126b c d x + 3 5 4 4 3 6 3 3 3 7 2 2 3 8 3 9 126b c d x + 84b c d x + 36b c d x + 9b c d x + b c * 3 3 3 2 2 2 3 a log(F) log(F) Ei((b d x + 3b c d x + 3b c d x + b c )log(F))%e / 10 9 9 8 2 8 7 3 7 6 4 6 5 5 5 4 18d x + 162c d x + 648c d x + 1512c d x + 2268c d x + 2268c d x + 6 4 3 7 3 2 8 2 9 1512c d x + 648c d x + 162c d x + 18c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^13, x)
(96) 3 9 9 3 8 8 3 2 7 7 3 3 6 6 3 4 5 5 - b d x - 9b c d x - 36b c d x - 84b c d x - 126b c d x + 3 5 4 4 3 6 3 3 3 7 2 2 3 8 3 9 - 126b c d x - 84b c d x - 36b c d x - 9b c d x - b c * 3 log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 - b d x - 6b c d x - 15b c d x - 20b c d x - 15b c d x + 2 5 2 6 - 6b c d x - b c * 2 log(F) + 3 3 2 2 2 3 (- 2b d x - 6b c d x - 6b c d x - 2b c )log(F) - 6 * 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) %e + 4 12 12 4 11 11 4 2 10 10 4 3 9 9 4 4 8 8 b d x + 12b c d x + 66b c d x + 220b c d x + 495b c d x + 4 5 7 7 4 6 6 6 4 7 5 5 4 8 4 4 4 9 3 3 792b c d x + 924b c d x + 792b c d x + 495b c d x + 220b c d x + 4 10 2 2 4 11 4 12 66b c d x + 12b c d x + b c * 4 3 3 2 2 2 3 a log(F) log(F) Ei((b d x + 3b c d x + 3b c d x + b c )log(F))%e / 13 12 12 11 2 11 10 3 10 9 4 9 8 72d x + 864c d x + 4752c d x + 15840c d x + 35640c d x + 5 8 7 6 7 6 7 6 5 8 5 4 9 4 3 57024c d x + 66528c d x + 57024c d x + 35640c d x + 15840c d x + 10 3 2 11 2 12 4752c d x + 864c d x + 72c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^16, x)
(97) 4 12 12 4 11 11 4 2 10 10 4 3 9 9 - b d x - 12b c d x - 66b c d x - 220b c d x + 4 4 8 8 4 5 7 7 4 6 6 6 4 7 5 5 - 495b c d x - 792b c d x - 924b c d x - 792b c d x + 4 8 4 4 4 9 3 3 4 10 2 2 4 11 4 12 - 495b c d x - 220b c d x - 66b c d x - 12b c d x - b c * 4 log(F) + 3 9 9 3 8 8 3 2 7 7 3 3 6 6 3 4 5 5 - b d x - 9b c d x - 36b c d x - 84b c d x - 126b c d x + 3 5 4 4 3 6 3 3 3 7 2 2 3 8 3 9 - 126b c d x - 84b c d x - 36b c d x - 9b c d x - b c * 3 log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 - 2b d x - 12b c d x - 30b c d x - 40b c d x - 30b c d x + 2 5 2 6 - 12b c d x - 2b c * 2 log(F) + 3 3 2 2 2 3 (- 6b d x - 18b c d x - 18b c d x - 6b c )log(F) - 24 * 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) %e + 5 15 15 5 14 14 5 2 13 13 5 3 12 12 b d x + 15b c d x + 105b c d x + 455b c d x + 5 4 11 11 5 5 10 10 5 6 9 9 5 7 8 8 1365b c d x + 3003b c d x + 5005b c d x + 6435b c d x + 5 8 7 7 5 9 6 6 5 10 5 5 5 11 4 4 6435b c d x + 5005b c d x + 3003b c d x + 1365b c d x + 5 12 3 3 5 13 2 2 5 14 5 15 455b c d x + 105b c d x + 15b c d x + b c * 5 3 3 2 2 2 3 a log(F) log(F) Ei((b d x + 3b c d x + 3b c d x + b c )log(F))%e / 16 15 15 14 2 14 13 3 13 12 360d x + 5400c d x + 37800c d x + 163800c d x + 4 12 11 5 11 10 6 10 9 7 9 8 491400c d x + 1081080c d x + 1801800c d x + 2316600c d x + 8 8 7 9 7 6 10 6 5 11 5 4 2316600c d x + 1801800c d x + 1081080c d x + 491400c d x + 12 4 3 13 3 2 14 2 15 163800c d x + 37800c d x + 5400c d x + 360c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) = 0.03 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^3, x)
(98) 3 3 2 2 2 3 (b d x + 3b c d x + 3b c d x + b c + a)log(F) (3d x + 3c)%e * +------------+ 3| 3 \|- b d log(F) + a log(F) 1 3 3 2 2 2 3 d %e Gamma(-,(- b d x - 3b c d x - 3b c d x - b c )log(F)) 3 / +------------+ 3| 3 9b d log(F)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^3)*(c+d*x), x)
a log(F) 2 3 3 2 2 2 3 d %e Gamma(-,(- b d x - 3b c d x - 3b c d x - b c )log(F)) 3 (99) - ------------------------------------------------------------------- +------------+2 3| 3 3\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3), x)
a log(F) 1 3 3 2 2 2 3 %e Gamma(-,(- b d x - 3b c d x - 3b c d x - b c )log(F)) 3 (100) - ----------------------------------------------------------------- +------------+ 3| 3 3\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^2, x)
(101) 3 3 2 2 2 3 +------------+2 (b d x + 3b c d x + 3b c d x + b c + a)log(F) 3| 3 - %e \|- b d log(F) + 3 2 a log(F) (- b d x - b c d )log(F)%e * 2 3 3 2 2 2 3 Gamma(-,(- b d x - 3b c d x - 3b c d x - b c )log(F)) 3 / +------------+2 2 3| 3 (d x + c d)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^3, x)
(102) 3 3 2 2 2 3 +------------+ (b d x + 3b c d x + 3b c d x + b c + a)log(F) 3| 3 - %e \|- b d log(F) + 3 2 2 2 a log(F) (- b d x - 2b c d x - b c d)log(F)%e * 1 3 3 2 2 2 3 Gamma(-,(- b d x - 3b c d x - 3b c d x - b c )log(F)) 3 / +------------+ 3 2 2 2 3| 3 (2d x + 4c d x + 2c d)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^5, x)
(103) 3 3 2 2 2 3 ((- 3b d x - 9b c d x - 9b c d x - 3b c )log(F) - 1) * 3 3 2 2 2 3 +------------+2 (b d x + 3b c d x + 3b c d x + b c + a)log(F) 3| 3 %e \|- b d log(F) + 2 6 4 2 5 3 2 2 4 2 2 3 3 2 4 2 2 (- 3b d x - 12b c d x - 18b c d x - 12b c d x - 3b c d )log(F) * a log(F) 2 3 3 2 2 2 3 %e Gamma(-,(- b d x - 3b c d x - 3b c d x - b c )log(F)) 3 / +------------+2 5 4 4 3 2 3 2 3 2 4 3| 3 (4d x + 16c d x + 24c d x + 16c d x + 4c d)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*(c+d*x)^(1/2)), x)
+-------+ +-------+ b log(f)\|d x + c + a log(f) (2b log(f)\|d x + c - 2)%e (104) -------------------------------------------------------- 2 2 b d log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*(c+d*x)^(1/3)), x)
(105) 2 2 3+-------+2 3+-------+ (3b log(f) \|d x + c - 6b log(f)\|d x + c + 6) * 3+-------+ b log(f)\|d x + c + a log(f) %e / 3 3 b d log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- n<0 integrate(F^(a+b/(c+d*x))*(c+d*x)^m, x)
%A a d + a c + b x ---------------- ++ %A d + c m (106) | F (%A d + c) d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x))*(c+d*x)^4, x)
(107) 4 4 4 3 2 2 3 3 2 3 (b d x + b c)log(F) + (b d x + 2b c d x + b c )log(F) + 2 3 3 2 2 2 2 2 2 3 2 (2b d x + 6b c d x + 6b c d x + 2b c )log(F) + 4 4 3 3 2 2 2 3 4 (6b d x + 24b c d x + 36b c d x + 24b c d x + 6b c )log(F) + 5 5 4 4 2 3 3 3 2 2 4 5 24d x + 120c d x + 240c d x + 240c d x + 120c d x + 24c * (a d x + a c + b)log(F) ----------------------- d x + c %e + 5 5 b log(F) a log(F) - b log(F) Ei(--------)%e d x + c / 120d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))*(c+d*x)^3, x)
(108) 3 3 3 2 2 2 2 2 2 2 (b d x + b c)log(F) + (b d x + 2b c d x + b c )log(F) + 3 3 2 2 2 3 4 4 3 3 (2b d x + 6b c d x + 6b c d x + 2b c )log(F) + 6d x + 24c d x + 2 2 2 3 4 36c d x + 24c d x + 6c * (a d x + a c + b)log(F) ----------------------- d x + c %e + 4 4 b log(F) a log(F) - b log(F) Ei(--------)%e d x + c / 24d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))*(c+d*x)^2, x)
(109) 2 2 2 2 2 2 3 3 (b d x + b c)log(F) + (b d x + 2b c d x + b c )log(F) + 2d x + 2 2 2 3 6c d x + 6c d x + 2c * (a d x + a c + b)log(F) ----------------------- d x + c %e + 3 3 b log(F) a log(F) - b log(F) Ei(--------)%e d x + c / 6d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))*(c+d*x), x)
(110) (a d x + a c + b)log(F) ----------------------- 2 2 2 d x + c ((b d x + b c)log(F) + d x + 2c d x + c )%e + 2 2 b log(F) a log(F) - b log(F) Ei(--------)%e d x + c / 2d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)), x)
(a d x + a c + b)log(F) ----------------------- d x + c b log(F) a log(F) (d x + c)%e - b log(F)Ei(--------)%e d x + c (111) ------------------------------------------------------------------- d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x))/(c+d*x), x)
b log(F) a log(F) Ei(--------)%e d x + c (112) - ---------------------- d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^2, x)
(a d x + a c + b)log(F) ----------------------- d x + c %e (113) - ------------------------- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^3, x)
(a d x + a c + b)log(F) ----------------------- d x + c (- b log(F) + d x + c)%e (114) ----------------------------------------------- 2 2 2 2 (b d x + b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^4, x)
(115) 2 2 2 2 2 (- b log(F) + (2b d x + 2b c)log(F) - 2d x - 4c d x - 2c ) * (a d x + a c + b)log(F) ----------------------- d x + c %e / 3 3 2 3 2 3 2 3 (b d x + 2b c d x + b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^5, x)
(116) 3 3 2 2 2 - b log(F) + (3b d x + 3b c)log(F) + 2 2 2 3 3 2 2 2 3 (- 6b d x - 12b c d x - 6b c )log(F) + 6d x + 18c d x + 18c d x + 6c * (a d x + a c + b)log(F) ----------------------- d x + c %e / 4 4 3 4 3 2 4 2 2 4 3 4 (b d x + 3b c d x + 3b c d x + b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^6, x)
(117) 4 4 3 3 3 - b log(F) + (4b d x + 4b c)log(F) + 2 2 2 2 2 2 2 (- 12b d x - 24b c d x - 12b c )log(F) + 3 3 2 2 2 3 4 4 3 3 (24b d x + 72b c d x + 72b c d x + 24b c )log(F) - 24d x - 96c d x + 2 2 2 3 4 - 144c d x - 96c d x - 24c * (a d x + a c + b)log(F) ----------------------- d x + c %e / 5 5 4 5 4 3 5 2 3 2 5 3 2 5 4 5 (b d x + 4b c d x + 6b c d x + 4b c d x + b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x))/(c+d*x)^7, x)
(118) 5 5 4 4 4 - b log(F) + (5b d x + 5b c)log(F) + 3 2 2 3 3 2 3 (- 20b d x - 40b c d x - 20b c )log(F) + 2 3 3 2 2 2 2 2 2 3 2 (60b d x + 180b c d x + 180b c d x + 60b c )log(F) + 4 4 3 3 2 2 2 3 4 (- 120b d x - 480b c d x - 720b c d x - 480b c d x - 120b c )log(F) + 5 5 4 4 2 3 3 3 2 2 4 5 120d x + 600c d x + 1200c d x + 1200c d x + 600c d x + 120c * (a d x + a c + b)log(F) ----------------------- d x + c %e / 6 6 5 6 5 4 6 2 4 3 6 3 3 2 6 4 2 6 5 6 (b d x + 5b c d x + 10b c d x + 10b c d x + 5b c d x + b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^m, x)
2 2 2 %A a d + 2%A a c d + a c + b ------------------------------ x 2 2 2 ++ %A d + 2%A c d + c m (119) | F (%A d + c) d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^9, x)
(120) 4 2 2 4 4 2 4 (b d x + 2b c d x + b c )log(F) + 3 4 4 3 3 3 3 2 2 2 3 3 3 4 3 (b d x + 4b c d x + 6b c d x + 4b c d x + b c )log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 2b d x + 12b c d x + 30b c d x + 40b c d x + 30b c d x + 2 5 2 6 12b c d x + 2b c * 2 log(F) + 8 8 7 7 2 6 6 3 5 5 4 4 4 6b d x + 48b c d x + 168b c d x + 336b c d x + 420b c d x + 5 3 3 6 2 2 7 8 336b c d x + 168b c d x + 48b c d x + 6b c * log(F) + 10 10 9 9 2 8 8 3 7 7 4 6 6 24d x + 240c d x + 1080c d x + 2880c d x + 5040c d x + 5 5 5 6 4 4 7 3 3 8 2 2 9 10 6048c d x + 5040c d x + 2880c d x + 1080c d x + 240c d x + 24c * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 d x + 2c d x + c %e + 5 5 b log(F) a log(F) - b log(F) Ei(------------------)%e 2 2 2 d x + 2c d x + c / 240d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^7, x)
(121) 3 2 2 3 3 2 3 (b d x + 2b c d x + b c )log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (b d x + 4b c d x + 6b c d x + 4b c d x + b c )log(F) + 6 6 5 5 2 4 4 3 3 3 4 2 2 2b d x + 12b c d x + 30b c d x + 40b c d x + 30b c d x + 5 6 12b c d x + 2b c * log(F) + 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6d x + 48c d x + 168c d x + 336c d x + 420c d x + 336c d x + 6 2 2 7 8 168c d x + 48c d x + 6c * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 d x + 2c d x + c %e + 4 4 b log(F) a log(F) - b log(F) Ei(------------------)%e 2 2 2 d x + 2c d x + c / 48d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^5, x)
(122) 2 2 2 2 2 2 2 (b d x + 2b c d x + b c )log(F) + 4 4 3 3 2 2 2 3 4 6 6 (b d x + 4b c d x + 6b c d x + 4b c d x + b c )log(F) + 2d x + 5 5 2 4 4 3 3 3 4 2 2 5 6 12c d x + 30c d x + 40c d x + 30c d x + 12c d x + 2c * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 d x + 2c d x + c %e + 3 3 b log(F) a log(F) - b log(F) Ei(------------------)%e 2 2 2 d x + 2c d x + c / 12d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^3, x)
(123) 2 2 2 4 4 3 3 2 2 2 3 (b d x + 2b c d x + b c )log(F) + d x + 4c d x + 6c d x + 4c d x + 4 c * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 d x + 2c d x + c %e + 2 2 b log(F) a log(F) - b log(F) Ei(------------------)%e 2 2 2 d x + 2c d x + c / 4d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x), x)
(124) 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 2 2 2 d x + 2c d x + c (d x + 2c d x + c )%e + b log(F) a log(F) - b log(F)Ei(------------------)%e 2 2 2 d x + 2c d x + c / 2d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x), x)
b log(F) a log(F) Ei(------------------)%e 2 2 2 d x + 2c d x + c (125) - -------------------------------- 2d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^3, x)
2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 d x + 2c d x + c %e (126) - -------------------------------------- 2b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^5, x)
(127) 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 2 2 2 d x + 2c d x + c (- b log(F) + d x + 2c d x + c )%e ----------------------------------------------------------------------- 2 3 2 2 2 2 2 2 (2b d x + 4b c d x + 2b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^7, x)
(128) 2 2 2 2 2 4 4 3 3 - b log(F) + (2b d x + 4b c d x + 2b c )log(F) - 2d x - 8c d x + 2 2 2 3 4 - 12c d x - 8c d x - 2c * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 d x + 2c d x + c %e / 3 5 4 3 4 3 3 2 3 2 3 3 2 3 4 3 (2b d x + 8b c d x + 12b c d x + 8b c d x + 2b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.01 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^9, x)
(129) 3 3 2 2 2 2 2 2 2 - b log(F) + (3b d x + 6b c d x + 3b c )log(F) + 4 4 3 3 2 2 2 3 4 6 6 (- 6b d x - 24b c d x - 36b c d x - 24b c d x - 6b c )log(F) + 6d x + 5 5 2 4 4 3 3 3 4 2 2 5 6 36c d x + 90c d x + 120c d x + 90c d x + 36c d x + 6c * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 d x + 2c d x + c %e / 4 7 6 4 6 5 4 2 5 4 4 3 4 3 4 4 3 2 4 5 2 2b d x + 12b c d x + 30b c d x + 40b c d x + 30b c d x + 12b c d x + 4 6 2b c d * 4 log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^11, x)
(130) 4 4 3 2 2 3 3 2 3 - b log(F) + (4b d x + 8b c d x + 4b c )log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 12b d x - 48b c d x - 72b c d x - 48b c d x - 12b c )log(F) + 6 6 5 5 2 4 4 3 3 3 4 2 2 24b d x + 144b c d x + 360b c d x + 480b c d x + 360b c d x + 5 6 144b c d x + 24b c * log(F) + 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 - 24d x - 192c d x - 672c d x - 1344c d x - 1680c d x - 1344c d x + 6 2 2 7 8 - 672c d x - 192c d x - 24c * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 d x + 2c d x + c %e / 5 9 8 5 8 7 5 2 7 6 5 3 6 5 5 4 5 4 2b d x + 16b c d x + 56b c d x + 112b c d x + 140b c d x + 5 5 4 3 5 6 3 2 5 7 2 5 8 112b c d x + 56b c d x + 16b c d x + 2b c d * 5 log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.04 (EV) = 0.05 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^13, x)
(131) 5 5 4 2 2 4 4 2 4 - b log(F) + (5b d x + 10b c d x + 5b c )log(F) + 3 4 4 3 3 3 3 2 2 2 3 3 3 4 3 (- 20b d x - 80b c d x - 120b c d x - 80b c d x - 20b c )log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 60b d x + 360b c d x + 900b c d x + 1200b c d x + 900b c d x + 2 5 2 6 360b c d x + 60b c * 2 log(F) + 8 8 7 7 2 6 6 3 5 5 - 120b d x - 960b c d x - 3360b c d x - 6720b c d x + 4 4 4 5 3 3 6 2 2 7 8 - 8400b c d x - 6720b c d x - 3360b c d x - 960b c d x - 120b c * log(F) + 10 10 9 9 2 8 8 3 7 7 4 6 6 120d x + 1200c d x + 5400c d x + 14400c d x + 25200c d x + 5 5 5 6 4 4 7 3 3 8 2 2 9 10 30240c d x + 25200c d x + 14400c d x + 5400c d x + 1200c d x + 120c * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 d x + 2c d x + c %e / 6 11 10 6 10 9 6 2 9 8 6 3 8 7 6 4 7 6 2b d x + 20b c d x + 90b c d x + 240b c d x + 420b c d x + 6 5 6 5 6 6 5 4 6 7 4 3 6 8 3 2 6 9 2 504b c d x + 420b c d x + 240b c d x + 90b c d x + 20b c d x + 6 10 2b c d * 6 log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.11 (EV) + 0.01 (OT) = 0.12 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^10, x)
(132) +----------+ | b log(F) d |- -------- | 2 6 6 +---+ a log(F) \| d - 32b log(F) \|%pi %e erf(--------------) d x + c + 5 2 5 5 (32b d x + 32b c d)log(F) + 4 4 3 4 3 2 4 2 2 4 3 4 (16b d x + 48b c d x + 48b c d x + 16b c d)log(F) + 3 6 5 3 5 4 3 2 4 3 3 3 3 2 3 4 2 24b d x + 120b c d x + 240b c d x + 240b c d x + 120b c d x + 3 5 24b c d * 3 log(F) + 2 8 7 2 7 6 2 2 6 5 2 3 5 4 60b d x + 420b c d x + 1260b c d x + 2100b c d x + 2 4 4 3 2 5 3 2 2 6 2 2 7 2100b c d x + 1260b c d x + 420b c d x + 60b c d * 2 log(F) + 10 9 9 8 2 8 7 3 7 6 210b d x + 1890b c d x + 7560b c d x + 17640b c d x + 4 6 5 5 5 4 6 4 3 7 3 2 26460b c d x + 26460b c d x + 17640b c d x + 7560b c d x + 8 2 9 1890b c d x + 210b c d * log(F) + 12 11 11 10 2 10 9 3 9 8 945d x + 10395c d x + 51975c d x + 155925c d x + 4 8 7 5 7 6 6 6 5 7 5 4 311850c d x + 436590c d x + 436590c d x + 311850c d x + 8 4 3 9 3 2 10 2 11 155925c d x + 51975c d x + 10395c d x + 945c d * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ d x + 2c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 | b log(F) 10395d |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) = 0.03 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^8, x)
(133) +----------+ | b log(F) d |- -------- | 2 5 5 +---+ a log(F) \| d - 16b log(F) \|%pi %e erf(--------------) d x + c + 4 2 4 4 (16b d x + 16b c d)log(F) + 3 4 3 3 3 2 3 2 2 3 3 3 (8b d x + 24b c d x + 24b c d x + 8b c d)log(F) + 2 6 5 2 5 4 2 2 4 3 2 3 3 2 2 4 2 12b d x + 60b c d x + 120b c d x + 120b c d x + 60b c d x + 2 5 12b c d * 2 log(F) + 8 7 7 6 2 6 5 3 5 4 30b d x + 210b c d x + 630b c d x + 1050b c d x + 4 4 3 5 3 2 6 2 7 1050b c d x + 630b c d x + 210b c d x + 30b c d * log(F) + 10 9 9 8 2 8 7 3 7 6 4 6 5 105d x + 945c d x + 3780c d x + 8820c d x + 13230c d x + 5 5 4 6 4 3 7 3 2 8 2 9 13230c d x + 8820c d x + 3780c d x + 945c d x + 105c d * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ d x + 2c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 | b log(F) 945d |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) = 0.03 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^6, x)
(134) +----------+ | b log(F) d |- -------- | 2 4 4 +---+ a log(F) \| d - 8b log(F) \|%pi %e erf(--------------) d x + c + 3 2 3 3 (8b d x + 8b c d)log(F) + 2 4 3 2 3 2 2 2 2 2 3 2 (4b d x + 12b c d x + 12b c d x + 4b c d)log(F) + 6 5 5 4 2 4 3 3 3 2 4 2 6b d x + 30b c d x + 60b c d x + 60b c d x + 30b c d x + 5 6b c d * log(F) + 8 7 7 6 2 6 5 3 5 4 4 4 3 5 3 2 15d x + 105c d x + 315c d x + 525c d x + 525c d x + 315c d x + 6 2 7 105c d x + 15c d * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ d x + 2c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 | b log(F) 105d |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^4, x)
(135) +----------+ | b log(F) d |- -------- | 2 3 3 +---+ a log(F) \| d - 4b log(F) \|%pi %e erf(--------------) d x + c + 2 2 2 2 (4b d x + 4b c d)log(F) + 4 3 3 2 2 2 3 6 5 5 4 (2b d x + 6b c d x + 6b c d x + 2b c d)log(F) + 3d x + 15c d x + 2 4 3 3 3 2 4 2 5 30c d x + 30c d x + 15c d x + 3c d * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ d x + 2c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 | b log(F) 15d |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^2, x)
(136) +----------+ | b log(F) d |- -------- | 2 2 2 +---+ a log(F) \| d - 2b log(F) \|%pi %e erf(--------------) d x + c + 2 4 3 3 2 2 2 3 ((2b d x + 2b c d)log(F) + d x + 3c d x + 3c d x + c d) * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ d x + 2c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 | b log(F) 3d |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2), x)
(137) +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d - b log(F)\|%pi %e erf(--------------) d x + c + 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ 2 d x + 2c d x + c | b log(F) (d x + c d)%e |- -------- | 2 \| d / +----------+ 2 | b log(F) d |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^2, x)
+----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d \|%pi %e erf(--------------) d x + c (138) - ----------------------------------- +----------+ 2 | b log(F) 2d |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^4, x)
(139) +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d (d x + c)\|%pi %e erf(--------------) d x + c + 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ d x + 2c d x + c | b log(F) - 2d %e |- -------- | 2 \| d / +----------+ 3 2 | b log(F) (4b d x + 4b c d )log(F) |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^6, x)
(140) +----------+ | b log(F) d |- -------- | 2 3 3 2 2 2 3 +---+ a log(F) \| d (- 3d x - 9c d x - 9c d x - 3c )\|%pi %e erf(--------------) d x + c + 3 2 2 2 (- 4b d log(F) + 6d x + 12c d x + 6c d) * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ d x + 2c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 5 3 2 4 2 2 2 3 2 3 2 2 | b log(F) (8b d x + 24b c d x + 24b c d x + 8b c d )log(F) |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^8, x)
(141) 5 5 4 4 2 3 3 3 2 2 4 5 +---+ (15d x + 75c d x + 150c d x + 150c d x + 75c d x + 15c )\|%pi * +----------+ | b log(F) d |- -------- | 2 a log(F) \| d %e erf(--------------) d x + c + 2 2 3 2 2 2 5 4 - 8b d log(F) + (20b d x + 40b c d x + 20b c d)log(F) - 30d x + 4 3 2 3 2 3 2 4 - 120c d x - 180c d x - 120c d x - 30c d * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ d x + 2c d x + c | b log(F) %e |- -------- | 2 \| d / 3 7 5 3 6 4 3 2 5 3 3 3 4 2 3 4 3 16b d x + 80b c d x + 160b c d x + 160b c d x + 80b c d x + 3 5 2 16b c d * +----------+ 3 | b log(F) log(F) |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) = 0.03 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^10, x)
(142) 7 7 6 6 2 5 5 3 4 4 4 3 3 - 105d x - 735c d x - 2205c d x - 3675c d x - 3675c d x + 5 2 2 6 7 - 2205c d x - 735c d x - 105c * +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d \|%pi %e erf(--------------) d x + c + 3 3 2 3 2 2 2 2 2 2 - 16b d log(F) + (56b d x + 112b c d x + 56b c d)log(F) + 5 4 4 3 2 3 2 3 2 4 (- 140b d x - 560b c d x - 840b c d x - 560b c d x - 140b c d) * log(F) + 7 6 6 5 2 5 4 3 4 3 4 3 2 210d x + 1260c d x + 3150c d x + 4200c d x + 3150c d x + 5 2 6 1260c d x + 210c d * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ d x + 2c d x + c | b log(F) %e |- -------- | 2 \| d / 4 9 7 4 8 6 4 2 7 5 4 3 6 4 4 4 5 3 32b d x + 224b c d x + 672b c d x + 1120b c d x + 1120b c d x + 4 5 4 2 4 6 3 4 7 2 672b c d x + 224b c d x + 32b c d * +----------+ 4 | b log(F) log(F) |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.05 (EV) = 0.05 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^12, x)
(143) 9 9 8 8 2 7 7 3 6 6 4 5 5 945d x + 8505c d x + 34020c d x + 79380c d x + 119070c d x + 5 4 4 6 3 3 7 2 2 8 9 119070c d x + 79380c d x + 34020c d x + 8505c d x + 945c * +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d \|%pi %e erf(--------------) d x + c + 4 4 3 3 2 3 2 3 2 3 - 32b d log(F) + (144b d x + 288b c d x + 144b c d)log(F) + 2 5 4 2 4 3 2 2 3 2 2 3 2 - 504b d x - 2016b c d x - 3024b c d x - 2016b c d x + 2 4 - 504b c d * 2 log(F) + 7 6 6 5 2 5 4 3 4 3 1260b d x + 7560b c d x + 18900b c d x + 25200b c d x + 4 3 2 5 2 6 18900b c d x + 7560b c d x + 1260b c d * log(F) + 9 8 8 7 2 7 6 3 6 5 4 5 4 - 1890d x - 15120c d x - 52920c d x - 105840c d x - 132300c d x + 5 4 3 6 3 2 7 2 8 - 105840c d x - 52920c d x - 15120c d x - 1890c d * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ d x + 2c d x + c | b log(F) %e |- -------- | 2 \| d / 5 11 9 5 10 8 5 2 9 7 5 3 8 6 5 4 7 5 64b d x + 576b c d x + 2304b c d x + 5376b c d x + 8064b c d x + 5 5 6 4 5 6 5 3 5 7 4 2 5 8 3 5 9 2 8064b c d x + 5376b c d x + 2304b c d x + 576b c d x + 64b c d * +----------+ 5 | b log(F) log(F) |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.07 (EV) + 0.01 (OT) = 0.08 sec
integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^14, x)
(144) 11 11 10 10 2 9 9 3 8 8 - 10395d x - 114345c d x - 571725c d x - 1715175c d x + 4 7 7 5 6 6 6 5 5 7 4 4 - 3430350c d x - 4802490c d x - 4802490c d x - 3430350c d x + 8 3 3 9 2 2 10 11 - 1715175c d x - 571725c d x - 114345c d x - 10395c * +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d \|%pi %e erf(--------------) d x + c + 5 5 4 3 2 4 2 4 2 4 - 64b d log(F) + (352b d x + 704b c d x + 352b c d)log(F) + 3 5 4 3 4 3 3 2 3 2 3 3 2 - 1584b d x - 6336b c d x - 9504b c d x - 6336b c d x + 3 4 - 1584b c d * 3 log(F) + 2 7 6 2 6 5 2 2 5 4 2 3 4 3 5544b d x + 33264b c d x + 83160b c d x + 110880b c d x + 2 4 3 2 2 5 2 2 6 83160b c d x + 33264b c d x + 5544b c d * 2 log(F) + 9 8 8 7 2 7 6 3 6 5 - 13860b d x - 110880b c d x - 388080b c d x - 776160b c d x + 4 5 4 5 4 3 6 3 2 - 970200b c d x - 776160b c d x - 388080b c d x + 7 2 8 - 110880b c d x - 13860b c d * log(F) + 11 10 10 9 2 9 8 3 8 7 20790d x + 207900c d x + 935550c d x + 2494800c d x + 4 7 6 5 6 5 6 5 4 7 4 3 4365900c d x + 5239080c d x + 4365900c d x + 2494800c d x + 8 3 2 9 2 10 935550c d x + 207900c d x + 20790c d * 2 2 2 (a d x + 2a c d x + a c + b)log(F) ------------------------------------ 2 2 2 +----------+ d x + 2c d x + c | b log(F) %e |- -------- | 2 \| d / 6 13 11 6 12 10 6 2 11 9 6 3 10 8 128b d x + 1408b c d x + 7040b c d x + 21120b c d x + 6 4 9 7 6 5 8 6 6 6 7 5 6 7 6 4 42240b c d x + 59136b c d x + 59136b c d x + 42240b c d x + 6 8 5 3 6 9 4 2 6 10 3 6 11 2 21120b c d x + 7040b c d x + 1408b c d x + 128b c d * +----------+ 6 | b log(F) log(F) |- -------- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.10 (EV) + 0.01 (OT) = 0.11 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^m, x)
3 3 2 2 2 3 %A a d + 3%A a c d + 3%A a c d + a c + b ------------------------------------------- x 3 3 2 2 2 3 ++ %A d + 3%A c d + 3%A c d + c m (145) | F (%A d + c) d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^14, x)
(146) 4 3 3 4 2 2 4 2 4 3 4 (b d x + 3b c d x + 3b c d x + b c )log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 b d x + 6b c d x + 15b c d x + 20b c d x + 15b c d x + 3 5 3 6 6b c d x + b c * 3 log(F) + 2 9 9 2 8 8 2 2 7 7 2 3 6 6 2 4 5 5 2b d x + 18b c d x + 72b c d x + 168b c d x + 252b c d x + 2 5 4 4 2 6 3 3 2 7 2 2 2 8 2 9 252b c d x + 168b c d x + 72b c d x + 18b c d x + 2b c * 2 log(F) + 12 12 11 11 2 10 10 3 9 9 6b d x + 72b c d x + 396b c d x + 1320b c d x + 4 8 8 5 7 7 6 6 6 7 5 5 2970b c d x + 4752b c d x + 5544b c d x + 4752b c d x + 8 4 4 9 3 3 10 2 2 11 12 2970b c d x + 1320b c d x + 396b c d x + 72b c d x + 6b c * log(F) + 15 15 14 14 2 13 13 3 12 12 4 11 11 24d x + 360c d x + 2520c d x + 10920c d x + 32760c d x + 5 10 10 6 9 9 7 8 8 8 7 7 72072c d x + 120120c d x + 154440c d x + 154440c d x + 9 6 6 10 5 5 11 4 4 12 3 3 120120c d x + 72072c d x + 32760c d x + 10920c d x + 13 2 2 14 15 2520c d x + 360c d x + 24c * 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e + 5 5 b log(F) a log(F) - b log(F) Ei(----------------------------)%e 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / 360d
Type: Union(Expression(Integer),...)
fricas
Time: 0.04 (EV) = 0.04 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^11, x)
(147) 3 3 3 3 2 2 3 2 3 3 3 (b d x + 3b c d x + 3b c d x + b c )log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 b d x + 6b c d x + 15b c d x + 20b c d x + 15b c d x + 2 5 2 6 6b c d x + b c * 2 log(F) + 9 9 8 8 2 7 7 3 6 6 4 5 5 2b d x + 18b c d x + 72b c d x + 168b c d x + 252b c d x + 5 4 4 6 3 3 7 2 2 8 9 252b c d x + 168b c d x + 72b c d x + 18b c d x + 2b c * log(F) + 12 12 11 11 2 10 10 3 9 9 4 8 8 6d x + 72c d x + 396c d x + 1320c d x + 2970c d x + 5 7 7 6 6 6 7 5 5 8 4 4 9 3 3 4752c d x + 5544c d x + 4752c d x + 2970c d x + 1320c d x + 10 2 2 11 12 396c d x + 72c d x + 6c * 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e + 4 4 b log(F) a log(F) - b log(F) Ei(----------------------------)%e 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / 72d
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) + 0.01 (OT) = 0.04 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^8, x)
(148) 2 3 3 2 2 2 2 2 2 3 2 (b d x + 3b c d x + 3b c d x + b c )log(F) + 6 6 5 5 2 4 4 3 3 3 4 2 2 b d x + 6b c d x + 15b c d x + 20b c d x + 15b c d x + 5 6 6b c d x + b c * log(F) + 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 2d x + 18c d x + 72c d x + 168c d x + 252c d x + 252c d x + 6 3 3 7 2 2 8 9 168c d x + 72c d x + 18c d x + 2c * 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e + 3 3 b log(F) a log(F) - b log(F) Ei(----------------------------)%e 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / 18d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^5, x)
(149) 3 3 2 2 2 3 6 6 5 5 (b d x + 3b c d x + 3b c d x + b c )log(F) + d x + 6c d x + 2 4 4 3 3 3 4 2 2 5 6 15c d x + 20c d x + 15c d x + 6c d x + c * 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e + 2 2 b log(F) a log(F) - b log(F) Ei(----------------------------)%e 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / 6d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^2, x)
(150) 3 3 2 2 2 3 (d x + 3c d x + 3c d x + c ) * 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e + b log(F) a log(F) - b log(F)Ei(----------------------------)%e 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / 3d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x), x)
b log(F) a log(F) Ei(----------------------------)%e 3 3 2 2 2 3 d x + 3c d x + 3c d x + c (151) - ------------------------------------------ 3d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^4, x)
3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e (152) - -------------------------------------------------- 3b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^7, x)
(153) 3 3 2 2 2 3 (- b log(F) + d x + 3c d x + 3c d x + c ) * 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e / 2 4 3 2 3 2 2 2 2 2 3 2 (3b d x + 9b c d x + 9b c d x + 3b c d)log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^10, x)
(154) 2 2 3 3 2 2 2 3 6 6 - b log(F) + (2b d x + 6b c d x + 6b c d x + 2b c )log(F) - 2d x + 5 5 2 4 4 3 3 3 4 2 2 5 6 - 12c d x - 30c d x - 40c d x - 30c d x - 12c d x - 2c * 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e / 3 7 6 3 6 5 3 2 5 4 3 3 4 3 3 4 3 2 3 5 2 3b d x + 18b c d x + 45b c d x + 60b c d x + 45b c d x + 18b c d x + 3 6 3b c d * 3 log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^13, x)
(155) 3 3 2 3 3 2 2 2 2 2 2 3 2 - b log(F) + (3b d x + 9b c d x + 9b c d x + 3b c )log(F) + 6 6 5 5 2 4 4 3 3 3 4 2 2 - 6b d x - 36b c d x - 90b c d x - 120b c d x - 90b c d x + 5 6 - 36b c d x - 6b c * log(F) + 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6d x + 54c d x + 216c d x + 504c d x + 756c d x + 756c d x + 6 3 3 7 2 2 8 9 504c d x + 216c d x + 54c d x + 6c * 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e / 4 10 9 4 9 8 4 2 8 7 4 3 7 6 4 4 6 5 3b d x + 27b c d x + 108b c d x + 252b c d x + 378b c d x + 4 5 5 4 4 6 4 3 4 7 3 2 4 8 2 4 9 378b c d x + 252b c d x + 108b c d x + 27b c d x + 3b c d * 4 log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.06 (EV) = 0.06 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^16, x)
(156) 4 4 3 3 3 3 2 2 3 2 3 3 3 - b log(F) + (4b d x + 12b c d x + 12b c d x + 4b c )log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 - 12b d x - 72b c d x - 180b c d x - 240b c d x - 180b c d x + 2 5 2 6 - 72b c d x - 12b c * 2 log(F) + 9 9 8 8 2 7 7 3 6 6 4 5 5 24b d x + 216b c d x + 864b c d x + 2016b c d x + 3024b c d x + 5 4 4 6 3 3 7 2 2 8 9 3024b c d x + 2016b c d x + 864b c d x + 216b c d x + 24b c * log(F) + 12 12 11 11 2 10 10 3 9 9 4 8 8 - 24d x - 288c d x - 1584c d x - 5280c d x - 11880c d x + 5 7 7 6 6 6 7 5 5 8 4 4 9 3 3 - 19008c d x - 22176c d x - 19008c d x - 11880c d x - 5280c d x + 10 2 2 11 12 - 1584c d x - 288c d x - 24c * 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e / 5 13 12 5 12 11 5 2 11 10 5 3 10 9 5 4 9 8 3b d x + 36b c d x + 198b c d x + 660b c d x + 1485b c d x + 5 5 8 7 5 6 7 6 5 7 6 5 5 8 5 4 5 9 4 3 2376b c d x + 2772b c d x + 2376b c d x + 1485b c d x + 660b c d x + 5 10 3 2 5 11 2 5 12 198b c d x + 36b c d x + 3b c d * 5 log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.11 (EV) + 0.01 (OT) = 0.13 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^19, x)
(157) 5 5 4 3 3 4 2 2 4 2 4 3 4 - b log(F) + (5b d x + 15b c d x + 15b c d x + 5b c )log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 - 20b d x - 120b c d x - 300b c d x - 400b c d x - 300b c d x + 3 5 3 6 - 120b c d x - 20b c * 3 log(F) + 2 9 9 2 8 8 2 2 7 7 2 3 6 6 2 4 5 5 60b d x + 540b c d x + 2160b c d x + 5040b c d x + 7560b c d x + 2 5 4 4 2 6 3 3 2 7 2 2 2 8 2 9 7560b c d x + 5040b c d x + 2160b c d x + 540b c d x + 60b c * 2 log(F) + 12 12 11 11 2 10 10 3 9 9 - 120b d x - 1440b c d x - 7920b c d x - 26400b c d x + 4 8 8 5 7 7 6 6 6 7 5 5 - 59400b c d x - 95040b c d x - 110880b c d x - 95040b c d x + 8 4 4 9 3 3 10 2 2 11 - 59400b c d x - 26400b c d x - 7920b c d x - 1440b c d x + 12 - 120b c * log(F) + 15 15 14 14 2 13 13 3 12 12 120d x + 1800c d x + 12600c d x + 54600c d x + 4 11 11 5 10 10 6 9 9 7 8 8 163800c d x + 360360c d x + 600600c d x + 772200c d x + 8 7 7 9 6 6 10 5 5 11 4 4 772200c d x + 600600c d x + 360360c d x + 163800c d x + 12 3 3 13 2 2 14 15 54600c d x + 12600c d x + 1800c d x + 120c * 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e / 6 16 15 6 15 14 6 2 14 13 6 3 13 12 3b d x + 45b c d x + 315b c d x + 1365b c d x + 6 4 12 11 6 5 11 10 6 6 10 9 6 7 9 8 4095b c d x + 9009b c d x + 15015b c d x + 19305b c d x + 6 8 8 7 6 9 7 6 6 10 6 5 6 11 5 4 19305b c d x + 15015b c d x + 9009b c d x + 4095b c d x + 6 12 4 3 6 13 3 2 6 14 2 6 15 1365b c d x + 315b c d x + 45b c d x + 3b c d * 6 log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.24 (EV) = 0.24 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^3, x)
(158) 3 2 6 4 5 3 2 4 2 3 3 4 2 ((3b d x + 3b c d )log(F) + d x + 4c d x + 6c d x + 4c d x + c d ) * 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 +----------+2 d x + 3c d x + 3c d x + c | b log(F) %e |- -------- 3| 3 \| d + 2 2 a log(F) 2 b log(F) 3b log(F) %e Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / +----------+2 3 | b log(F) 4d |- -------- 3| 3 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x)^3)*(c+d*x), x)
(159) 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 3 2 2 2 d x + 3c d x + 3c d x + c (d x + 2c d x + c d)%e * +----------+ | b log(F) |- -------- 3| 3 \| d + a log(F) 1 b log(F) b log(F)%e Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / +----------+ 2 | b log(F) 2d |- -------- 3| 3 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3), x)
(160) 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 3 2 d x + 3c d x + 3c d x + c (d x + c d )%e * +----------+2 | b log(F) |- -------- 3| 3 \| d + a log(F) 2 b log(F) b log(F)%e Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / +----------+2 3 | b log(F) d |- -------- 3| 3 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^2, x)
a log(F) 1 b log(F) %e Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 d x + 3c d x + 3c d x + c (161) ------------------------------------------------- +----------+ 2 | b log(F) 3d |- -------- 3| 3 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^3, x)
a log(F) 2 b log(F) %e Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 d x + 3c d x + 3c d x + c (162) ------------------------------------------------- +----------+2 3 | b log(F) 3d |- -------- 3| 3 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^5, x)
(163) 3 3 2 2 2 3 (a d x + 3a c d x + 3a c d x + a c + b)log(F) ------------------------------------------------ 3 3 2 2 2 3 +----------+ d x + 3c d x + 3c d x + c | b log(F) - 3d %e |- -------- 3| 3 \| d + a log(F) 1 b log(F) (- d x - c)%e Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / +----------+ 3 2 | b log(F) (9b d x + 9b c d )log(F) |- -------- 3| 3 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.01 (EV) = 0.02 sec
-- n symbolic integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^m, x)
x n ++ m b (%A d + c) + a (164) | (%A d + c) F d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^3, x)
x n ++ 3 3 2 2 2 3 b (%A d + c) + a (165) | (%A d + 3%A c d + 3%A c d + c )F d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^2, x)
x n ++ 2 2 2 b (%A d + c) + a (166) | (%A d + 2%A c d + c )F d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x), x)
x n ++ b (%A d + c) + a (167) | (%A d + c)F d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n), x)
x n ++ b (%A d + c) + a (168) | F d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n)/(c+d*x), x)
a log(F) n log(d x + c) %e Ei(b log(F)%e ) (169) -------------------------------------- d n
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^2, x)
n x b (%A d + c) + a ++ F (170) | -------------------- d%A ++ 2 2 2 %A d + 2%A c d + c
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^3, x)
n x b (%A d + c) + a ++ F (171) | ------------------------------- d%A ++ 3 3 2 2 2 3 %A d + 3%A c d + 3%A c d + c
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^4, x)
n x b (%A d + c) + a ++ F (172) | ------------------------------------------ d%A ++ 4 4 3 3 2 2 2 3 4 %A d + 4%A c d + 6%A c d + 4%A c d + c
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+6*n), x)
(173) 5 5 n log(d x + c) 5 4 4 n log(d x + c) 4 b log(F) (%e ) - 5b log(F) (%e ) + 3 3 n log(d x + c) 3 2 2 n log(d x + c) 2 20b log(F) (%e ) - 60b log(F) (%e ) + n log(d x + c) 120b log(F)%e - 120 * n log(d x + c) b log(F)%e + a log(F) %e / 6 6 b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+5*n), x)
(174) 4 4 n log(d x + c) 4 3 3 n log(d x + c) 3 b log(F) (%e ) - 4b log(F) (%e ) + 2 2 n log(d x + c) 2 n log(d x + c) 12b log(F) (%e ) - 24b log(F)%e + 24 * n log(d x + c) b log(F)%e + a log(F) %e / 5 5 b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+4*n), x)
(175) 3 3 n log(d x + c) 3 2 2 n log(d x + c) 2 b log(F) (%e ) - 3b log(F) (%e ) + n log(d x + c) 6b log(F)%e - 6 * n log(d x + c) b log(F)%e + a log(F) %e / 4 4 b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+3*n), x)
(176) 2 2 n log(d x + c) 2 n log(d x + c) (b log(F) (%e ) - 2b log(F)%e + 2) * n log(d x + c) b log(F)%e + a log(F) %e / 3 3 b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+2*n), x)
n log(d x + c) n log(d x + c) b log(F)%e + a log(F) (b log(F)%e - 1)%e (177) ------------------------------------------------------------------- 2 2 b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+n), x)
n log(d x + c) b log(F)%e + a log(F) %e (178) ------------------------------------- b d n log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)/(c+d*x), x)
a log(F) n log(d x + c) %e Ei(b log(F)%e ) (179) -------------------------------------- d n
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-n), x)
(180) n log(d x + c) b log(F)%e + a log(F) - %e + a log(F) n log(d x + c) n log(d x + c) b log(F)%e %e Ei(b log(F)%e ) / n log(d x + c) d n %e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-2*n), x)
(181) n log(d x + c) n log(d x + c) b log(F)%e + a log(F) (- b log(F)%e - 1)%e + 2 2 a log(F) n log(d x + c) 2 n log(d x + c) b log(F) %e (%e ) Ei(b log(F)%e ) / n log(d x + c) 2 2d n (%e )
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-3*n), x)
(182) 2 2 n log(d x + c) 2 n log(d x + c) (- b log(F) (%e ) - b log(F)%e - 2) * n log(d x + c) b log(F)%e + a log(F) %e + 3 3 a log(F) n log(d x + c) 3 n log(d x + c) b log(F) %e (%e ) Ei(b log(F)%e ) / n log(d x + c) 3 6d n (%e )
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-4*n), x)
(183) 3 3 n log(d x + c) 3 2 2 n log(d x + c) 2 - b log(F) (%e ) - b log(F) (%e ) + n log(d x + c) - 2b log(F)%e - 6 * n log(d x + c) b log(F)%e + a log(F) %e + 4 4 a log(F) n log(d x + c) 4 n log(d x + c) b log(F) %e (%e ) Ei(b log(F)%e ) / n log(d x + c) 4 24d n (%e )
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-5*n), x)
(184) 4 4 n log(d x + c) 4 3 3 n log(d x + c) 3 - b log(F) (%e ) - b log(F) (%e ) + 2 2 n log(d x + c) 2 n log(d x + c) - 2b log(F) (%e ) - 6b log(F)%e - 24 * n log(d x + c) b log(F)%e + a log(F) %e + 5 5 a log(F) n log(d x + c) 5 n log(d x + c) b log(F) %e (%e ) Ei(b log(F)%e ) / n log(d x + c) 5 120d n (%e )
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x)^n)*(a+b*x)^(-1+1/2*n), x)
(n - 2)log(b x + a) ------------------- +---+ 2 +----------+ \|%pi erf((b x + a)%e \|- c log(F) ) (185) ------------------------------------------------------ +----------+ b n\|- c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (IN) = 0.02 sec
integrate((a+b*x)^(-1+1/2*n)/F^(c*(a+b*x)^n), x)
(n - 2)log(b x + a) ------------------- +---+ 2 +--------+ \|%pi erf((b x + a)%e \|c log(F) ) (186) ---------------------------------------------------- +--------+ b n\|c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
-- Integrands of the form (e+f x)^m F^(a+b (c+d x)^n)
-- n>0 integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^5, x)
(187) 3 5 5 3 4 2 4 3 3 3 2 3 3 2 4 3 2 - 4b c d f + 20b c d e f - 40b c d e f + 40b c d e f + 3 5 4 3 6 5 - 20b c d e f + 4b d e * 3 log(F) + 2 3 5 2 2 2 4 2 3 2 3 2 4 3 2 2 (20b c d f - 60b c d e f + 60b c d e f - 20b d e f )log(F) + 5 2 4 (- 15b c d f + 15b d e f )log(F) * +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) \|%pi %e erf(------------------------) d + 2 4 5 4 2 3 5 2 4 4 3 4b d f x + (- 4b c d f + 20b d e f )x + 2 2 2 5 2 3 4 2 4 2 3 2 (4b c d f - 20b c d e f + 40b d e f )x + 2 3 5 2 2 2 4 2 3 2 3 2 4 3 2 (- 4b c d f + 20b c d e f - 40b c d e f + 40b d e f )x + 2 4 5 2 3 4 2 2 2 2 3 2 3 3 2 2 4 4 4b c f - 20b c d e f + 40b c d e f - 40b c d e f + 20b d e f * 2 log(F) + 2 5 2 5 2 4 2 5 - 8b d f x + (14b c d f - 30b d e f )x - 18b c f + 4 2 2 3 50b c d e f - 40b d e f * log(F) + 5 8f * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 3 6 3 | 2 8b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^4, x)
(188) 2 4 4 2 3 2 3 2 2 3 2 2 2 4 3 2 5 4 (4b c d f - 16b c d e f + 24b c d e f - 16b c d e f + 4b d e ) * 2 log(F) + 2 4 2 3 3 2 2 4 (- 12b c d f + 24b c d e f - 12b d e f )log(F) + 3d f * +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) \|%pi %e erf(------------------------) d + 3 4 3 2 4 3 3 2 4b d f x + (- 4b c d f + 16b d e f )x + 2 4 2 3 3 2 2 3 4 2 3 (4b c d f - 16b c d e f + 24b d e f )x - 4b c f + 16b c d e f + 2 2 2 3 3 - 24b c d e f + 16b d e f * log(F) + 4 4 3 - 6d f x + 10c f - 16d e f * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 2 5 2 | 2 8b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^3, x)
(189) 2 3 3 2 2 2 2 2 3 2 2 4 3 2 (- 2b c d f + 6b c d e f - 6b c d e f + 2b d e )log(F) + 3 2 2 (3b c d f - 3b d e f )log(F) * +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) \|%pi %e erf(------------------------) d + 2 3 2 3 2 2 2 3 2 2b d f x + (- 2b c d f + 6b d e f )x + 2b c f - 6b c d e f + 2 2 6b d e f * log(F) + 3 - 2f * 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 2 4 2 | 2 4b d log(F) \|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^2, x)
(190) 2 2 2 3 2 2 +---+ a log(F) ((2b c d f - 4b c d e f + 2b d e )log(F) - d f )\|%pi %e * +------------+ | 2 (d x + c)\|- b d log(F) erf(------------------------) d + 2 2 2 2 2 (b d x + 2b c d x + b c + a)log(F) (2d f x - 2c f + 4d e f)%e * +------------+ | 2 \|- b d log(F) / +------------+ 3 | 2 4b d log(F)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)*(e+f*x), x)
(191) +------------+ | 2 2 +---+ a log(F) (d x + c)\|- b d log(F) (- b c d f + b d e)log(F)\|%pi %e erf(------------------------) d + 2 2 2 +------------+ (b d x + 2b c d x + b c + a)log(F) | 2 f %e \|- b d log(F) / +------------+ 2 | 2 2b d log(F)\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2), x)
+------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) \|%pi %e erf(------------------------) d (192) --------------------------------------------- +------------+ | 2 2\|- b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x)^2)/(e+f*x), x)
2 2 2 x %A b d + 2%A b c d + b c + a ++ F (193) | ------------------------------- d%A ++ %A f + e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)/(e+f*x)^2, x)
2 2 2 x %A b d + 2%A b c d + b c + a ++ F (194) | ------------------------------- d%A ++ 2 2 2 %A f + 2%A e f + e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x)^2)/(e+f*x)^3, x)
2 2 2 x %A b d + 2%A b c d + b c + a ++ F (195) | ------------------------------- d%A ++ 3 3 2 2 2 3 %A f + 3%A e f + 3%A e f + e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e*(c+d*x)^3)*(a+b*x)^3, x)
(196) 3 3 2 2 2 3 +-----+2 3 2 3 d e x + 3c d e x + 3c d e x + c e 3| 3 (3b d x + 9a b d - 6b c)%e \|- d e + 3 4 2 3 2 2 2 3 3 3 ((- 3a d + 9a b c d - 9a b c d + 3b c d)e + b d) * +-----+ 1 3 3 2 2 2 3 3| 3 Gamma(-,- d e x - 3c d e x - 3c d e x - c e)\|- d e 3 + 2 4 2 3 3 2 2 (- 9a b d + 18a b c d - 9b c d )e * 2 3 3 2 2 2 3 Gamma(-,- d e x - 3c d e x - 3c d e x - c e) 3 / +-----+2 4 3| 3 9d e \|- d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e*(c+d*x)^3)*(a+b*x)^2, x)
(197) 3 3 2 2 2 3 +-----+2 2 d e x + 3c d e x + 3c d e x + c e 3| 3 b %e \|- d e + 2 3 2 2 2 (- a d + 2a b c d - b c d)e * +-----+ 1 3 3 2 2 2 3 3| 3 Gamma(-,- d e x - 3c d e x - 3c d e x - c e)\|- d e 3 + 3 2 2 2 3 3 2 2 2 3 (- 2a b d + 2b c d )e Gamma(-,- d e x - 3c d e x - 3c d e x - c e) 3 / +-----+2 3 3| 3 3d e \|- d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(%e^(e*(c+d*x)^3)*(a+b*x), x)
(198) +-----+ 1 3 3 2 2 2 3 3| 3 (- a d + b c)Gamma(-,- d e x - 3c d e x - 3c d e x - c e)\|- d e 3 + 2 3 3 2 2 2 3 - b d Gamma(-,- d e x - 3c d e x - 3c d e x - c e) 3 / +-----+2 3| 3 3d \|- d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e*(c+d*x)^3), x)
1 3 3 2 2 2 3 Gamma(-,- d e x - 3c d e x - 3c d e x - c e) 3 (199) - ---------------------------------------------- +-----+ 3| 3 3\|- d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e*(c+d*x)^3)/(a+b*x), x)
3 3 2 2 2 3 x (%A d + 3%A c d + 3%A c d + c )e ++ %e (200) | ------------------------------------ d%A ++ %A b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e*(c+d*x)^3)/(a+b*x)^2, x)
3 3 2 2 2 3 x (%A d + 3%A c d + 3%A c d + c )e ++ %e (201) | ------------------------------------ d%A ++ 2 2 2 %A b + 2%A a b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
-- n<0 integrate(F^(a+b/(c+d*x))/(e+f*x), x)
(202) ((a c + b)f - a d e)log(F) -------------------------- (- b d f x - b d e)log(F) c f - d e Ei(----------------------------)%e 2 2 (c d f - d e)x + c f - c d e + b log(F) a log(F) - Ei(--------)%e d x + c / f
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))/(e+f*x)^2, x)
(203) (- b d f x - b d e)log(F) (- b d f x - b d e)log(F)Ei(----------------------------) 2 2 (c d f - d e)x + c f - c d e * ((a c + b)f - a d e)log(F) -------------------------- c f - d e %e + (a d x + a c + b)log(F) ----------------------- 2 2 d x + c ((- c d f + d e)x - c f + c d e)%e / 2 3 2 2 2 2 2 2 2 3 (c f - 2c d e f + d e f)x + c e f - 2c d e f + d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b/(c+d*x))/(e+f*x)^3, x)
(204) 2 2 3 2 2 2 2 2 2 2 2 (b d f x + 2b d e f x + b d e f)log(F) + 2 3 3 2 2 2 2 3 2 (2b c d f - 2b d e f )x + (4b c d e f - 4b d e f)x + 2 2 3 3 2b c d e f - 2b d e * log(F) * ((a c + b)f - a d e)log(F) -------------------------- (- b d f x - b d e)log(F) c f - d e Ei(----------------------------)%e 2 2 (c d f - d e)x + c f - c d e + 2 3 3 2 2 2 3 3 2 2 2 (b c d f - b d e f )x + (b c d f - b d e f)x + b c d e f + 2 2 - b c d e f * log(F) + 2 2 3 3 2 4 2 2 2 2 2 3 2 4 3 (c d f - 2c d e f + d e f)x + (2c d e f - 4c d e f + 2d e )x + 4 3 3 2 2 2 2 3 3 - c f + 4c d e f - 5c d e f + 2c d e * (a d x + a c + b)log(F) ----------------------- d x + c %e / 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 (2c f - 8c d e f + 12c d e f - 8c d e f + 2d e f )x + 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4 2 4 (4c e f - 16c d e f + 24c d e f - 16c d e f + 4d e f)x + 2c e f + 3 3 3 2 2 4 2 3 5 4 6 - 8c d e f + 12c d e f - 8c d e f + 2d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(F^(a+b/(c+d*x))/(e+f*x)^4, x)
(205) 3 3 5 3 3 3 4 2 3 3 2 3 3 3 3 2 3 (- b d f x - 3b d e f x - 3b d e f x - b d e f )log(F) + 2 3 5 2 4 4 3 2 3 4 2 4 2 3 2 (- 6b c d f + 6b d e f )x + (- 18b c d e f + 18b d e f )x + 2 3 2 3 2 4 3 2 2 3 3 2 2 4 4 (- 18b c d e f + 18b d e f )x - 6b c d e f + 6b d e f * 2 log(F) + 2 3 5 4 4 5 2 3 3 (- 6b c d f + 12b c d e f - 6b d e f )x + 2 3 4 4 2 3 5 3 2 2 (- 18b c d e f + 36b c d e f - 18b d e f )x + 2 3 2 3 4 3 2 5 4 2 3 3 2 (- 18b c d e f + 36b c d e f - 18b d e f)x - 6b c d e f + 4 4 5 5 12b c d e f - 6b d e * log(F) * ((a c + b)f - a d e)log(F) -------------------------- (- b d f x - b d e)log(F) c f - d e Ei(----------------------------)%e 2 2 (c d f - d e)x + c f - c d e + 2 3 5 2 4 4 3 (- b c d f + b d e f )x + 2 2 2 5 2 3 4 2 4 2 3 2 (- b c d f - b c d e f + 2b d e f )x + 2 2 2 4 2 3 2 3 2 4 3 2 2 2 2 2 3 2 3 3 2 (- 2b c d e f + b c d e f + b d e f )x - b c d e f + b c d e f * 2 log(F) + 2 3 5 4 4 5 2 3 3 (- 5b c d f + 10b c d e f - 5b d e f )x + 3 2 5 2 3 4 4 2 3 5 3 2 2 (- 4b c d f - 3b c d e f + 18b c d e f - 11b d e f )x + 4 5 3 2 4 2 3 2 3 4 3 2 b c d f - 12b c d e f + 15b c d e f + 2b c d e f + 5 4 - 6b d e f * x + 4 4 3 2 2 3 2 3 3 2 4 4 b c d e f - 8b c d e f + 13b c d e f - 6b c d e f * log(F) + 3 3 5 2 4 4 5 2 3 6 3 2 3 (- 2c d f + 6c d e f - 6c d e f + 2d e f )x + 3 3 4 2 4 2 3 5 3 2 6 4 2 (- 6c d e f + 18c d e f - 18c d e f + 6d e f)x + 3 3 2 3 2 4 3 2 5 4 6 5 6 5 5 4 (- 6c d e f + 18c d e f - 18c d e f + 6d e )x - 2c f + 12c d e f + 4 2 2 3 3 3 3 2 2 4 4 5 5 - 30c d e f + 38c d e f - 24c d e f + 6c d e * (a d x + a c + b)log(F) ----------------------- d x + c %e / 6 9 5 8 4 2 2 7 3 3 3 6 2 4 4 5 6c f - 36c d e f + 90c d e f - 120c d e f + 90c d e f + 5 5 4 6 6 3 - 36c d e f + 6d e f * 3 x + 6 8 5 2 7 4 2 3 6 3 3 4 5 2 4 5 4 18c e f - 108c d e f + 270c d e f - 360c d e f + 270c d e f + 5 6 3 6 7 2 - 108c d e f + 18d e f * 2 x + 6 2 7 5 3 6 4 2 4 5 3 3 5 4 2 4 6 3 18c e f - 108c d e f + 270c d e f - 360c d e f + 270c d e f + 5 7 2 6 8 - 108c d e f + 18d e f * x + 6 3 6 5 4 5 4 2 5 4 3 3 6 3 2 4 7 2 5 8 6c e f - 36c d e f + 90c d e f - 120c d e f + 90c d e f - 36c d e f + 6 9 6d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) + 0.01 (OT) = 0.04 sec
integrate(%e^(e/(c+d*x))*(a+b*x)^4, x)
(206) 4 5 5 4 4 3 5 4 24b d x + (6b d e + 120a b d )x + 4 3 2 3 4 4 3 2 2 5 3 (2b d e + (40a b d - 16b c d )e + 240a b d )x + 4 2 3 3 3 4 2 2 b d e + (20a b d - 14b c d )e + 2 2 4 3 3 4 2 2 3 5 (120a b d - 120a b c d + 36b c d )e + 240a b d * 2 x + 4 4 3 2 4 3 b d e + (20a b d - 18b c d)e + 2 2 3 3 2 4 2 2 (120a b d - 200a b c d + 86b c d)e + 3 4 2 2 3 3 2 2 4 3 4 5 (240a b d - 480a b c d + 360a b c d - 96b c d)e + 120a d * x + 4 4 3 4 2 3 b c e + (20a b c d - 19b c )e + 2 2 2 3 2 4 3 2 (120a b c d - 220a b c d + 102b c )e + 3 3 2 2 2 2 3 3 4 4 4 4 (240a b c d - 600a b c d + 520a b c d - 154b c )e + 120a c d + 3 2 3 2 2 3 2 3 4 4 5 - 240a b c d + 240a b c d - 120a b c d + 24b c * e ------- d x + c %e + 4 5 3 4 4 - b e + (- 20a b d + 20b c)e + 2 2 2 3 4 2 3 (- 120a b d + 240a b c d - 120b c )e + 3 3 2 2 2 3 2 4 3 2 (- 240a b d + 720a b c d - 720a b c d + 240b c )e + 4 4 3 3 2 2 2 2 3 3 4 4 (- 120a d + 480a b c d - 720a b c d + 480a b c d - 120b c )e * e Ei(-------) d x + c / 5 120d
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) = 0.03 sec
integrate(%e^(e/(c+d*x))*(a+b*x)^3, x)
(207) 3 4 4 3 3 2 4 3 6b d x + (2b d e + 24a b d )x + 3 2 2 2 3 3 2 2 4 2 (b d e + (12a b d - 6b c d )e + 36a b d )x + 3 3 2 2 3 2 b d e + (12a b d - 10b c d)e + 2 3 2 2 3 2 3 4 (36a b d - 48a b c d + 18b c d)e + 24a d * x + 3 3 2 3 2 2 2 2 2 2 3 3 b c e + (12a b c d - 11b c )e + (36a b c d - 60a b c d + 26b c )e + 3 3 2 2 2 2 3 3 4 24a c d - 36a b c d + 24a b c d - 6b c * e ------- d x + c %e + 3 4 2 3 3 2 2 2 3 2 2 - b e + (- 12a b d + 12b c)e + (- 36a b d + 72a b c d - 36b c )e + 3 3 2 2 2 2 3 3 (- 24a d + 72a b c d - 72a b c d + 24b c )e * e Ei(-------) d x + c / 4 24d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(%e^(e/(c+d*x))*(a+b*x)^2, x)
(208) 2 3 3 2 2 3 2 2b d x + (b d e + 6a b d )x + 2 2 2 2 2 3 2 2 (b d e + (6a b d - 4b c d)e + 6a d )x + b c e + 2 2 2 2 2 2 3 (6a b c d - 5b c )e + 6a c d - 6a b c d + 2b c * e ------- d x + c %e + 2 3 2 2 2 2 2 2 e (- b e + (- 6a b d + 6b c)e + (- 6a d + 12a b c d - 6b c )e)Ei(-------) d x + c / 3 6d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e/(c+d*x))*(a+b*x), x)
(209) e ------- 2 2 2 2 d x + c (b d x + (b d e + 2a d )x + b c e + 2a c d - b c )%e + 2 e (- b e + (- 2a d + 2b c)e)Ei(-------) d x + c / 2 2d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e/(c+d*x)), x)
e ------- d x + c e (d x + c)%e - e Ei(-------) d x + c (210) ---------------------------------- d
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(e/(c+d*x))/(a+b*x), x)
b e - --------- b d e x + a d e a d - b c e Ei(------------------------------)%e - Ei(-------) 2 2 d x + c (a d - b c d)x + a c d - b c (211) ------------------------------------------------------------- b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(%e^(e/(c+d*x))/(a+b*x)^2, x)
(212) e ------- 2 2 d x + c ((a d - b c d)x + a c d - b c )%e + b e - --------- b d e x + a d e a d - b c (- b d e x - a d e)Ei(------------------------------)%e 2 2 (a d - b c d)x + a c d - b c / 2 2 2 3 2 3 2 2 2 2 (a b d - 2a b c d + b c )x + a d - 2a b c d + a b c
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x))/(a+b*x)^3, x)
(213) 2 3 3 2 2 4 2 3 3 2 2 2 ((- a b d + b c d )e + a b d - 2a b c d + b c d )x + 2 3 3 2 3 4 2 3 2 2 2 ((- a b d + b c d)e + 2a d - 4a b c d + 2a b c d )x + 2 2 2 2 3 3 2 2 2 2 3 3 4 (- a b c d + a b c d)e + 2a c d - 5a b c d + 4a b c d - b c * e ------- d x + c %e + 3 2 2 2 3 3 2 2 (b d e + (- 2a b d + 2b c d )e)x + 2 2 2 2 3 2 2 2 2 2 (2a b d e + (- 4a b d + 4a b c d )e)x + a b d e + 3 3 2 2 (- 2a d + 2a b c d )e * b e - --------- b d e x + a d e a d - b c Ei(------------------------------)%e 2 2 (a d - b c d)x + a c d - b c / 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c )x + 5 4 4 2 3 3 3 2 2 2 4 3 5 4 6 4 (4a b d - 16a b c d + 24a b c d - 16a b c d + 4a b c )x + 2a d + 5 3 4 2 2 2 3 3 3 2 4 4 - 8a b c d + 12a b c d - 8a b c d + 2a b c
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(%e^(e/(c+d*x)^2)*(a+b*x)^3, x)
(214) 2 3 2 3 3 2 2 2 2 3 3 ((- 8a b d + 8b c)e + (- 4a d + 12a b c d - 12a b c d + 4b c )e) * +----+ | e d |- -- | 2 +---+ \| d \|%pi erf(--------) d x + c + 3 5 4 2 5 3 3 3 2 5 2 b d x + 4a b d x + (b d e + 6a b d )x + 2 3 3 2 3 5 2 2 3 2 3 4 ((8a b d - 6b c d )e + 4a d )x + (8a b c d - 7b c d)e + 4a c d + 2 2 3 2 3 2 3 4 - 6a b c d + 4a b c d - b c d * e ------------------ 2 2 2 d x + 2c d x + c %e + 3 2 2 3 2 2 3 2 e (- b d e + (- 6a b d + 12a b c d - 6b c d)e)Ei(------------------) 2 2 2 d x + 2c d x + c * +----+ | e |- -- | 2 \| d / +----+ 5 | e 4d |- -- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(%e^(e/(c+d*x)^2)*(a+b*x)^2, x)
(215) +----+ | e d |- -- | 2 2 2 2 2 2 2 +---+ \| d (- 2b e + (- 3a d + 6a b c d - 3b c )e)\|%pi erf(--------) d x + c + 2 4 3 4 2 2 2 2 4 2 2 3 b d x + 3a b d x + (2b d e + 3a d )x + 2b c d e + 3a c d + 2 2 2 3 - 3a b c d + b c d * e ------------------ 2 2 2 d x + 2c d x + c %e + 2 2 e (- 3a b d + 3b c d)e Ei(------------------) 2 2 2 d x + 2c d x + c * +----+ | e |- -- | 2 \| d / +----+ 4 | e 3d |- -- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)^2)*(a+b*x), x)
(216) +----+ | e d |- -- | 2 +---+ \| d (- 2a d + 2b c)e\|%pi erf(--------) d x + c + e ------------------ 2 2 2 3 2 3 2 2 d x + 2c d x + c (b d x + 2a d x + 2a c d - b c d)%e + e - b d e Ei(------------------) 2 2 2 d x + 2c d x + c * +----+ | e |- -- | 2 \| d / +----+ 3 | e 2d |- -- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)^2), x)
+----+ | e e d |- -- ------------------ | 2 2 2 2 +----+ +---+ \| d 2 d x + 2c d x + c | e - e\|%pi erf(--------) + (d x + c d)%e |- -- d x + c | 2 \| d (217) --------------------------------------------------------------- +----+ 2 | e d |- -- | 2 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)^2)/(a+b*x), x)
e -------------------- 2 2 2 x %A d + 2%A c d + c ++ %e (218) | ---------------------- d%A ++ %A b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)^2)/(a+b*x)^2, x)
e -------------------- 2 2 2 x %A d + 2%A c d + c ++ %e (219) | ---------------------- d%A ++ 2 2 2 %A b + 2%A a b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(%e^(e/(c+d*x)^2)/(a+b*x)^3, x)
e -------------------- 2 2 2 x %A d + 2%A c d + c ++ %e (220) | ------------------------------- d%A ++ 3 3 2 2 2 3 %A b + 3%A a b + 3%A a b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(%e^(e/(c+d*x)^3)*(a+b*x)^3, x)
(221) 3 6 4 2 6 3 2 6 2 3 3 3 6 3 2 b d x + 4a b d x + 6a b d x + (3b d e + 4a d )x + 3b c d e + 3 5 2 2 4 2 3 3 3 4 2 4a c d - 6a b c d + 4a b c d - b c d * e ---------------------------- 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e + 2 3 3 2 e (- 4a b d + 4b c d )e Ei(----------------------------) 3 3 2 2 2 3 d x + 3c d x + 3c d x + c * +----+2 | e |- -- 3| 3 \| d + 2 3 2 2 3 2 (6a b d - 12a b c d + 6b c d)e * +----+ 1 e | e Gamma(-,- ----------------------------) |- -- 3 3 3 2 2 2 3 3| 3 d x + 3c d x + 3c d x + c \| d + 3 2 3 3 2 2 2 2 3 3 (3b e + (4a d - 12a b c d + 12a b c d - 4b c )e) * 2 e Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / +----+2 6 | e 4d |- -- 3| 3 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(%e^(e/(c+d*x)^3)*(a+b*x)^2, x)
(222) 2 5 3 5 2 2 5 2 4 2 3 2 3 2 (b d x + 3a b d x + 3a d x + 3a c d - 3a b c d + b c d ) * e ---------------------------- 3 3 2 2 2 3 d x + 3c d x + 3c d x + c %e + 2 2 e - b d e Ei(----------------------------) 3 3 2 2 2 3 d x + 3c d x + 3c d x + c * +----+2 | e |- -- 3| 3 \| d + +----+ 2 2 1 e | e (3a b d - 3b c d)e Gamma(-,- ----------------------------) |- -- 3 3 3 2 2 2 3 3| 3 d x + 3c d x + 3c d x + c \| d + 2 2 2 2 2 e (3a d - 6a b c d + 3b c )e Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / +----+2 5 | e 3d |- -- 3| 3 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)^3)*(a+b*x), x)
(223) e ---------------------------- 3 3 2 2 2 3 4 2 4 3 2 2 d x + 3c d x + 3c d x + c (b d x + 2a d x + 2a c d - b c d )%e * +----+2 | e |- -- 3| 3 \| d + +----+ 1 e | e b d e Gamma(-,- ----------------------------) |- -- 3 3 3 2 2 2 3 3| 3 d x + 3c d x + 3c d x + c \| d + 2 e (2a d - 2b c)e Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / +----+2 4 | e 2d |- -- 3| 3 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(%e^(e/(c+d*x)^3), x)
(224) e ---------------------------- 3 3 2 2 2 3 +----+2 3 2 d x + 3c d x + 3c d x + c | e (d x + c d )%e |- -- 3| 3 \| d + 2 e e Gamma(-,- ----------------------------) 3 3 3 2 2 2 3 d x + 3c d x + 3c d x + c / +----+2 3 | e d |- -- 3| 3 \| d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(e/(c+d*x)^3)/(a+b*x), x)
e ------------------------------- 3 3 2 2 2 3 x %A d + 3%A c d + 3%A c d + c ++ %e (225) | --------------------------------- d%A ++ %A b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(%e^(e/(c+d*x)^3)/(a+b*x)^2, x)
e ------------------------------- 3 3 2 2 2 3 x %A d + 3%A c d + 3%A c d + c ++ %e (226) | --------------------------------- d%A ++ 2 2 2 %A b + 2%A a b + a
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec




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