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Examples involving exponential function from Albert Rich testsuite.

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-- Integration Problems Involving Exponentials
-- Integrands of the form u F^(c (a+b x))
-- Integrands of the form (d+e x)^m F^(c (a+b x)) integrate(F^(c*(a+b*x))*(d+e*x)^m, x)
x ++ (%A b + a)c m (1) | F (%A e + d) d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.04 (IN) + 0.01 (EV) + 0.23 (OT) = 0.28 sec
integrate(F^(c*(a+b*x))*(d+e*x)^4, x)
(2) 4 4 4 4 4 4 3 3 4 4 2 2 2 4 4 3 4 4 4 4 (b c e x + 4b c d e x + 6b c d e x + 4b c d e x + b c d )log(F) + 3 3 4 3 3 3 3 2 3 3 2 2 3 3 3 3 (- 4b c e x - 12b c d e x - 12b c d e x - 4b c d e)log(F) + 2 2 4 2 2 2 3 2 2 2 2 2 (12b c e x + 24b c d e x + 12b c d e )log(F) + 4 3 4 (- 24b c e x - 24b c d e )log(F) + 24e * (b c x + a c)log(F) %e / 5 5 5 b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) + 0.01 (EV) = 0.02 sec
integrate(F^(c*(a+b*x))*(d+e*x)^3, x)
(3) 3 3 3 3 3 3 2 2 3 3 2 3 3 3 3 (b c e x + 3b c d e x + 3b c d e x + b c d )log(F) + 2 2 3 2 2 2 2 2 2 2 2 (- 3b c e x - 6b c d e x - 3b c d e)log(F) + 3 2 3 (6b c e x + 6b c d e )log(F) - 6e * (b c x + a c)log(F) %e / 4 4 4 b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*(d+e*x)^2, x)
(4) 2 2 2 2 2 2 2 2 2 2 2 (b c e x + 2b c d e x + b c d )log(F) + (- 2b c e x - 2b c d e)log(F) + 2 2e * (b c x + a c)log(F) %e / 3 3 3 b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x), x)
(b c x + a c)log(F) ((b c e x + b c d)log(F) - e)%e (5) -------------------------------------------------- 2 2 2 b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x)), x)
(b c x + a c)log(F) %e (6) --------------------- b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d+e*x), x)
(a c e - b c d)log(F) --------------------- (b c e x + b c d)log(F) e Ei(-----------------------)%e e (7) -------------------------------------------------- e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^2, x)
(8) (b c x + a c)log(F) - e %e + (a c e - b c d)log(F) --------------------- (b c e x + b c d)log(F) e (b c e x + b c d)log(F)Ei(-----------------------)%e e / 3 2 e x + d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^3, x)
(9) 2 2 (b c x + a c)log(F) ((- b c e x - b c d e)log(F) - e )%e + 2 2 2 2 2 2 2 2 2 2 (b c e x + b c d)log(F) (b c e x + 2b c d e x + b c d )log(F) Ei(-----------------------) e * (a c e - b c d)log(F) --------------------- e %e / 5 2 4 2 3 2e x + 4d e x + 2d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^4, x)
(10) 2 2 3 2 2 2 2 2 2 2 2 (- b c e x - 2b c d e x - b c d e)log(F) + 3 2 3 (- b c e x - b c d e )log(F) - 2e * (b c x + a c)log(F) %e + 3 3 3 3 3 3 2 2 3 3 2 3 3 3 3 (b c e x + 3b c d e x + 3b c d e x + b c d )log(F) * (a c e - b c d)log(F) --------------------- (b c e x + b c d)log(F) e Ei(-----------------------)%e e / 7 3 6 2 2 5 3 4 6e x + 18d e x + 18d e x + 6d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d+e*x)^5, x)
(11) 3 3 4 3 3 3 3 2 3 3 2 2 3 3 3 3 (- b c e x - 3b c d e x - 3b c d e x - b c d e)log(F) + 2 2 4 2 2 2 3 2 2 2 2 2 (- b c e x - 2b c d e x - b c d e )log(F) + 4 3 4 (- 2b c e x - 2b c d e )log(F) - 6e * (b c x + a c)log(F) %e + 4 4 4 4 4 4 3 3 4 4 2 2 2 4 4 3 4 4 4 4 (b c e x + 4b c d e x + 6b c d e x + 4b c d e x + b c d )log(F) * (a c e - b c d)log(F) --------------------- (b c e x + b c d)log(F) e Ei(-----------------------)%e e / 9 4 8 3 2 7 2 3 6 4 5 24e x + 96d e x + 144d e x + 96d e x + 24d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d^4+4*d^3*e*x+6*d^2*e^2*x^2+4*d*e^3*x^3+e^4*x^4), x)
(12) 4 4 4 4 4 4 3 3 4 4 2 2 2 4 4 3 4 4 4 4 (b c e x + 4b c d e x + 6b c d e x + 4b c d e x + b c d )log(F) + 3 3 4 3 3 3 3 2 3 3 2 2 3 3 3 3 (- 4b c e x - 12b c d e x - 12b c d e x - 4b c d e)log(F) + 2 2 4 2 2 2 3 2 2 2 2 2 (12b c e x + 24b c d e x + 12b c d e )log(F) + 4 3 4 (- 24b c e x - 24b c d e )log(F) + 24e * (b c x + a c)log(F) %e / 5 5 5 b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(c*(a+b*x))*(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3), x)
(13) 3 3 3 3 3 3 2 2 3 3 2 3 3 3 3 (b c e x + 3b c d e x + 3b c d e x + b c d )log(F) + 2 2 3 2 2 2 2 2 2 2 2 (- 3b c e x - 6b c d e x - 3b c d e)log(F) + 3 2 3 (6b c e x + 6b c d e )log(F) - 6e * (b c x + a c)log(F) %e / 4 4 4 b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(F^(c*(a+b*x))*(d^2+2*d*e*x+e^2*x^2), x)
(14) 2 2 2 2 2 2 2 2 2 2 2 (b c e x + 2b c d e x + b c d )log(F) + (- 2b c e x - 2b c d e)log(F) + 2 2e * (b c x + a c)log(F) %e / 3 3 3 b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d^2+2*d*e*x+e^2*x^2), x)
(15) (b c x + a c)log(F) - e %e + (a c e - b c d)log(F) --------------------- (b c e x + b c d)log(F) e (b c e x + b c d)log(F)Ei(-----------------------)%e e / 3 2 e x + d e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3), x)
(16) 2 2 (b c x + a c)log(F) ((- b c e x - b c d e)log(F) - e )%e + 2 2 2 2 2 2 2 2 2 2 (b c e x + b c d)log(F) (b c e x + 2b c d e x + b c d )log(F) Ei(-----------------------) e * (a c e - b c d)log(F) --------------------- e %e / 5 2 4 2 3 2e x + 4d e x + 2d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d^4+4*d^3*e*x+6*d^2*e^2*x^2+4*d*e^3*x^3+e^4*x^4), x)
(17) 2 2 3 2 2 2 2 2 2 2 2 (- b c e x - 2b c d e x - b c d e)log(F) + 3 2 3 (- b c e x - b c d e )log(F) - 2e * (b c x + a c)log(F) %e + 3 3 3 3 3 3 2 2 3 3 2 3 3 3 3 (b c e x + 3b c d e x + 3b c d e x + b c d )log(F) * (a c e - b c d)log(F) --------------------- (b c e x + b c d)log(F) e Ei(-----------------------)%e e / 7 3 6 2 2 5 3 4 6e x + 18d e x + 18d e x + 6d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d^5+5*d^4*e*x+10*d^3*e^2*x^2+10*d^2*e^3*x^3+5*d*e^4*x^4+e^5*x^5), x)
(18) 3 3 4 3 3 3 3 2 3 3 2 2 3 3 3 3 (- b c e x - 3b c d e x - 3b c d e x - b c d e)log(F) + 2 2 4 2 2 2 3 2 2 2 2 2 (- b c e x - 2b c d e x - b c d e )log(F) + 4 3 4 (- 2b c e x - 2b c d e )log(F) - 6e * (b c x + a c)log(F) %e + 4 4 4 4 4 4 3 3 4 4 2 2 2 4 4 3 4 4 4 4 (b c e x + 4b c d e x + 6b c d e x + 4b c d e x + b c d )log(F) * (a c e - b c d)log(F) --------------------- (b c e x + b c d)log(F) e Ei(-----------------------)%e e / 9 4 8 3 2 7 2 3 6 4 5 24e x + 96d e x + 144d e x + 96d e x + 24d e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*((d+e*x)^n)^m, x)
x ++ (%A b + a)c m n (19) | F (%A e + d) d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d^4+4*d^3*e*x+6*d^2*e^2*x^2+4*d*e^3*x^3+e^4*x^4)^m, x)
x ++ (%A b + a)c 4 4 3 3 2 2 2 3 4 m (20) | F (%A e + 4%A d e + 6%A d e + 4%A d e + d ) d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3)^m, x)
x ++ (%A b + a)c 3 3 2 2 2 3 m (21) | F (%A e + 3%A d e + 3%A d e + d ) d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d^2+2*d*e*x+e^2*x^2)^m, x)
x ++ (%A b + a)c 2 2 2 m (22) | F (%A e + 2%A d e + d ) d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x)^m, x)
x ++ (%A b + a)c m (23) | F (%A e + d) d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d+e*x)^m, x)
x (%A b + a)c ++ F (24) | ------------ d%A ++ m (%A e + d)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(c*(a+b*x))/(d^2+2*d*e*x+e^2*x^2)^m, x)
x (%A b + a)c ++ F (25) | ----------------------- d%A ++ 2 2 2 m (%A e + 2%A d e + d )
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d^3+3*d^2*e*x+3*d*e^2*x^2+e^3*x^3)^m, x)
x (%A b + a)c ++ F (26) | ---------------------------------- d%A ++ 3 3 2 2 2 3 m (%A e + 3%A d e + 3%A d e + d )
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(2+5*x), x)
(5x + 2)log(F) %e (27) ---------------- 5log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*x), x)
(b x + a)log(F) %e (28) ----------------- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(10^(2+5*x), x)
(5x + 2)log(10) %e (29) ----------------- 5log(10)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- Integrands of the form (d+e x)^(m/2) F^(c (a+b x)) integrate(F^(a+b*x)*x^(7/2), x)
(30) +---+ a log(F) +-+ +----------+ 105\|%pi %e erf(\|x \|- b log(F) ) + 3 3 3 2 2 2 +-+ (16b x log(F) - 56b x log(F) + 140b x log(F) - 210)\|x * (b x + a)log(F) +----------+ %e \|- b log(F) / 4 4 +----------+ 16b log(F) \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(a+b*x)*x^(5/2), x)
(31) +---+ a log(F) +-+ +----------+ - 15\|%pi %e erf(\|x \|- b log(F) ) + 2 2 2 +-+ (b x + a)log(F) +----------+ (8b x log(F) - 20b x log(F) + 30)\|x %e \|- b log(F) / 3 3 +----------+ 8b log(F) \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*x)*x^(3/2), x)
(32) +---+ a log(F) +-+ +----------+ 3\|%pi %e erf(\|x \|- b log(F) ) + +-+ (b x + a)log(F) +----------+ (4b x log(F) - 6)\|x %e \|- b log(F) / 2 2 +----------+ 4b log(F) \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*x)*x^(1/2), x)
(33) +---+ a log(F) +-+ +----------+ - \|%pi %e erf(\|x \|- b log(F) ) + +-+ (b x + a)log(F) +----------+ 2\|x %e \|- b log(F) / +----------+ 2b log(F)\|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*x)/x^(1/2), x)
+---+ a log(F) +-+ +----------+ \|%pi %e erf(\|x \|- b log(F) ) (34) -------------------------------------- +----------+ \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*x)/x^(3/2), x)
(35) +---+ +-+ a log(F) +-+ +----------+ 2b log(F)\|%pi \|x %e erf(\|x \|- b log(F) ) + (b x + a)log(F) +----------+ - 2%e \|- b log(F) / +-+ +----------+ \|x \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*x)/x^(5/2), x)
(36) 2 2 +---+ +-+ a log(F) +-+ +----------+ 4b x log(F) \|%pi \|x %e erf(\|x \|- b log(F) ) + (b x + a)log(F) +----------+ (- 4b x log(F) - 2)%e \|- b log(F) / +-+ +----------+ 3x\|x \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*x)/x^(7/2), x)
(37) 3 2 3 +---+ +-+ a log(F) +-+ +----------+ 8b x log(F) \|%pi \|x %e erf(\|x \|- b log(F) ) + 2 2 2 (b x + a)log(F) +----------+ (- 8b x log(F) - 4b x log(F) - 6)%e \|- b log(F) / 2 +-+ +----------+ 15x \|x \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*x)/x^(9/2), x)
(38) 4 3 4 +---+ +-+ a log(F) +-+ +----------+ 16b x log(F) \|%pi \|x %e erf(\|x \|- b log(F) ) + 3 3 3 2 2 2 (b x + a)log(F) (- 16b x log(F) - 8b x log(F) - 12b x log(F) - 30)%e * +----------+ \|- b log(F) / 3 +-+ +----------+ 105x \|x \|- b log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x)^(7/2), x)
(39) (a c e - b c d)log(F) --------------------- +------------+ 3 +---+ e +-------+ | b c log(F) 105e \|%pi %e erf(\|e x + d |- ---------- ) \| e + 3 3 3 3 3 3 2 2 3 3 2 3 3 3 3 (16b c e x + 48b c d e x + 48b c d e x + 16b c d )log(F) + 2 2 3 2 2 2 2 2 2 2 2 (- 56b c e x - 112b c d e x - 56b c d e)log(F) + 3 2 3 (140b c e x + 140b c d e )log(F) - 210e * +------------+ +-------+ (b c x + a c)log(F) | b c log(F) \|e x + d %e |- ---------- \| e / +------------+ 4 4 4 | b c log(F) 16b c log(F) |- ---------- \| e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x)^(5/2), x)
(40) (a c e - b c d)log(F) --------------------- +------------+ 2 +---+ e +-------+ | b c log(F) - 15e \|%pi %e erf(\|e x + d |- ---------- ) \| e + 2 2 2 2 2 2 2 2 2 2 (8b c e x + 16b c d e x + 8b c d )log(F) + 2 2 (- 20b c e x - 20b c d e)log(F) + 30e * +------------+ +-------+ (b c x + a c)log(F) | b c log(F) \|e x + d %e |- ---------- \| e / +------------+ 3 3 3 | b c log(F) 8b c log(F) |- ---------- \| e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x)^(3/2), x)
(41) (a c e - b c d)log(F) --------------------- +------------+ +---+ e +-------+ | b c log(F) 3e\|%pi %e erf(\|e x + d |- ---------- ) \| e + +-------+ (b c x + a c)log(F) ((4b c e x + 4b c d)log(F) - 6e)\|e x + d %e * +------------+ | b c log(F) |- ---------- \| e / +------------+ 2 2 2 | b c log(F) 4b c log(F) |- ---------- \| e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x)^(1/2), x)
(42) (a c e - b c d)log(F) --------------------- +------------+ +---+ e +-------+ | b c log(F) - \|%pi %e erf(\|e x + d |- ---------- ) \| e + +------------+ +-------+ (b c x + a c)log(F) | b c log(F) 2\|e x + d %e |- ---------- \| e / +------------+ | b c log(F) 2b c log(F) |- ---------- \| e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^(1/2), x)
(a c e - b c d)log(F) --------------------- +------------+ +---+ e +-------+ | b c log(F) \|%pi %e erf(\|e x + d |- ---------- ) \| e (43) ----------------------------------------------------------- +------------+ | b c log(F) e |- ---------- \| e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))/(d+e*x)^(3/2), x)
(44) (a c e - b c d)log(F) --------------------- +---+ +-------+ e 2b c log(F)\|%pi \|e x + d %e * +------------+ +-------+ | b c log(F) erf(\|e x + d |- ---------- ) \| e + +------------+ (b c x + a c)log(F) | b c log(F) - 2e %e |- ---------- \| e / +------------+ 2 +-------+ | b c log(F) e \|e x + d |- ---------- \| e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^(5/2), x)
(45) (a c e - b c d)log(F) --------------------- 2 2 2 2 2 +---+ +-------+ e (4b c e x + 4b c d)log(F) \|%pi \|e x + d %e * +------------+ +-------+ | b c log(F) erf(\|e x + d |- ---------- ) \| e + +------------+ 2 2 (b c x + a c)log(F) | b c log(F) ((- 4b c e x - 4b c d e)log(F) - 2e )%e |- ---------- \| e / +------------+ 4 3 +-------+ | b c log(F) (3e x + 3d e )\|e x + d |- ---------- \| e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^(7/2), x)
(46) 3 3 2 2 3 3 3 3 2 3 +---+ +-------+ (8b c e x + 16b c d e x + 8b c d )log(F) \|%pi \|e x + d * (a c e - b c d)log(F) --------------------- +------------+ e +-------+ | b c log(F) %e erf(\|e x + d |- ---------- ) \| e + 2 2 3 2 2 2 2 2 2 2 2 (- 8b c e x - 16b c d e x - 8b c d e)log(F) + 3 2 3 (- 4b c e x - 4b c d e )log(F) - 6e * +------------+ (b c x + a c)log(F) | b c log(F) %e |- ---------- \| e / +------------+ 6 2 5 2 4 +-------+ | b c log(F) (15e x + 30d e x + 15d e )\|e x + d |- ---------- \| e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))/(d+e*x)^(9/2), x)
(47) 4 4 3 3 4 4 2 2 4 4 2 4 4 3 4 +---+ (16b c e x + 48b c d e x + 48b c d e x + 16b c d )log(F) \|%pi * (a c e - b c d)log(F) --------------------- +------------+ +-------+ e +-------+ | b c log(F) \|e x + d %e erf(\|e x + d |- ---------- ) \| e + 3 3 4 3 3 3 3 2 3 3 2 2 3 3 3 3 (- 16b c e x - 48b c d e x - 48b c d e x - 16b c d e)log(F) + 2 2 4 2 2 2 3 2 2 2 2 2 (- 8b c e x - 16b c d e x - 8b c d e )log(F) + 4 3 4 (- 12b c e x - 12b c d e )log(F) - 30e * +------------+ (b c x + a c)log(F) | b c log(F) %e |- ---------- \| e / +------------+ 8 3 7 2 2 6 3 5 +-------+ | b c log(F) (105e x + 315d e x + 315d e x + 105d e )\|e x + d |- ---------- \| e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(x^(13/2)/%e^(b*x), x)
(48) b x +---+ +-+ +-+ 135135%e \|%pi erf(\|b \|x ) + 6 6 5 5 4 4 3 3 2 2 - 128b x - 832b x - 4576b x - 20592b x - 72072b x - 180180b x + - 270270 * +-+ +-+ \|b \|x / 7 b x +-+ 128b %e \|b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
-- Integrands of the form Px F^(c (a+b x)) integrate(F^(c*(a+b*x))*(d+e*x), x)
(b c x + a c)log(F) ((b c e x + b c d)log(F) - e)%e (49) -------------------------------------------------- 2 2 2 b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*(d+e*x+f*x^2), x)
(50) 2 2 2 2 2 2 2 2 ((b c f x + b c e x + b c d)log(F) + (- 2b c f x - b c e)log(F) + 2f) * (b c x + a c)log(F) %e / 3 3 3 b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*(d+e*x+f*x^2+g*x^3), x)
(51) 3 3 3 3 3 2 3 3 3 3 3 (b c g x + b c f x + b c e x + b c d)log(F) + 2 2 2 2 2 2 2 2 (- 3b c g x - 2b c f x - b c e)log(F) + (6b c g x + 2b c f)log(F) - 6g * (b c x + a c)log(F) %e / 4 4 4 b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*(d+e*x+f*x^2+g*x^3+h*x^4), x)
(52) 4 4 4 4 4 3 4 4 2 4 4 4 4 4 (b c h x + b c g x + b c f x + b c e x + b c d)log(F) + 3 3 3 3 3 2 3 3 3 3 3 (- 4b c h x - 3b c g x - 2b c f x - b c e)log(F) + 2 2 2 2 2 2 2 2 (12b c h x + 6b c g x + 2b c f)log(F) + (- 24b c h x - 6b c g)log(F) + 24h * (b c x + a c)log(F) %e / 5 5 5 b c log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- Integrands of the form x^m (e+f x)^n F^(a+b (c+d x)) integrate(%e^(-a-b*x)*x^m*(a+b*x)^3, x)
x ++ 3 3 2 2 2 3 - %A b - a m (53) | (%A b + 3%A a b + 3%A a b + a )%e %A d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*x^3*(a+b*x)^3, x)
(54) 6 6 5 5 2 4 4 - b x + (- 3a - 6)b x + (- 3a - 15a - 30)b x + 3 2 3 3 3 2 2 2 (- a - 12a - 60a - 120)b x + (- 3a - 36a - 180a - 360)b x + 3 2 3 2 (- 6a - 72a - 360a - 720)b x - 6a - 72a - 360a - 720 * - b x - a %e / 4 b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*x^2*(a+b*x)^3, x)
(55) 5 5 4 4 2 3 3 - b x + (- 3a - 5)b x + (- 3a - 12a - 20)b x + 3 2 2 2 3 2 3 (- a - 9a - 36a - 60)b x + (- 2a - 18a - 72a - 120)b x - 2a + 2 - 18a - 72a - 120 * - b x - a %e / 3 b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(%e^(-a-b*x)*x*(a+b*x)^3, x)
(56) 4 4 3 3 2 2 2 - b x + (- 3a - 4)b x + (- 3a - 9a - 12)b x + 3 2 3 2 (- a - 6a - 18a - 24)b x - a - 6a - 18a - 24 * - b x - a %e / 2 b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^3, x)
(57) 3 3 2 2 2 3 2 (- b x + (- 3a - 3)b x + (- 3a - 6a - 6)b x - a - 3a - 6a - 6) * - b x - a %e / b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*(a+b*x)^3/x, x)
3 - a 2 2 2 - b x - a (58) a Ei(- b x)%e + (- b x + (- 3a - 2)b x - 3a - 3a - 2)%e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^3/x^2, x)
(59) 3 2 - a 2 2 3 - b x - a (- a + 3a )b x Ei(- b x)%e + (- b x + (- 3a - 1)b x - a )%e ------------------------------------------------------------------------- x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*(a+b*x)^3/x^3, x)
(60) 3 2 2 2 - a 2 2 3 2 3 - b x - a (a - 6a + 6a)b x Ei(- b x)%e + (- 2b x + (a - 6a )b x - a )%e ----------------------------------------------------------------------------- 2 2x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^3/x^4, x)
(61) 3 2 3 3 - a (- a + 9a - 18a + 6)b x Ei(- b x)%e + 3 2 2 2 3 2 3 - b x - a ((- a + 9a - 18a)b x + (a - 9a )b x - 2a )%e / 3 6x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x))*x^m*(e+f*x)^2, x)
x ++ 2 2 2 m %A b d + b c + a (62) | (%A f + 2%A e f + e )%A F d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x))*x^3*(e+f*x)^2, x)
(63) 5 5 2 5 5 5 4 5 5 2 3 5 (b d f x + 2b d e f x + b d e x )log(F) + 4 4 2 4 4 4 3 4 4 2 2 4 (- 5b d f x - 8b d e f x - 3b d e x )log(F) + 3 3 2 3 3 3 2 3 3 2 3 (20b d f x + 24b d e f x + 6b d e x)log(F) + 2 2 2 2 2 2 2 2 2 2 (- 60b d f x - 48b d e f x - 6b d e )log(F) + 2 2 (120b d f x + 48b d e f)log(F) - 120f * (b d x + b c + a)log(F) %e / 6 6 6 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.05 (EV) = 0.05 sec
integrate(F^(a+b*(c+d*x))*x^2*(e+f*x)^2, x)
(64) 4 4 2 4 4 4 3 4 4 2 2 4 (b d f x + 2b d e f x + b d e x )log(F) + 3 3 2 3 3 3 2 3 3 2 3 (- 4b d f x - 6b d e f x - 2b d e x)log(F) + 2 2 2 2 2 2 2 2 2 2 (12b d f x + 12b d e f x + 2b d e )log(F) + 2 2 (- 24b d f x - 12b d e f)log(F) + 24f * (b d x + b c + a)log(F) %e / 5 5 5 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x))*x*(e+f*x)^2, x)
(65) 3 3 2 3 3 3 2 3 3 2 3 (b d f x + 2b d e f x + b d e x)log(F) + 2 2 2 2 2 2 2 2 2 2 (- 3b d f x - 4b d e f x - b d e )log(F) + 2 2 (6b d f x + 4b d e f)log(F) - 6f * (b d x + b c + a)log(F) %e / 4 4 4 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x))*(e+f*x)^2, x)
(66) 2 2 2 2 2 2 2 2 2 2 2 (b d f x + 2b d e f x + b d e )log(F) + (- 2b d f x - 2b d e f)log(F) + 2 2f * (b d x + b c + a)log(F) %e / 3 3 3 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x, x)
(67) 2 2 (b d x + b c + a)log(F) ((b d f x + 2b d e f)log(F) - f )%e + 2 2 2 2 (b c + a)log(F) b d e log(F) Ei(b d x log(F))%e / 2 2 2 b d log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^2, x)
(68) 2 2 (b d x + b c + a)log(F) (- b d e log(F) + f x)%e + 2 2 2 2 (b c + a)log(F) (b d e x log(F) + 2b d e f x log(F))Ei(b d x log(F))%e / b d x log(F)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^3, x)
(69) 2 2 (b d x + b c + a)log(F) (- b d e x log(F) - 4e f x - e )%e + 2 2 2 2 2 2 2 2 (b d e x log(F) + 4b d e f x log(F) + 2f x )Ei(b d x log(F)) * (b c + a)log(F) %e / 2 2x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^4, x)
(70) 2 2 2 2 2 2 2 2 2 - b d e x log(F) + (- 6b d e f x - b d e x)log(F) - 6f x - 6e f x + 2 - 2e * (b d x + b c + a)log(F) %e + 3 3 2 3 3 2 2 3 2 2 3 (b d e x log(F) + 6b d e f x log(F) + 6b d f x log(F)) * (b c + a)log(F) Ei(b d x log(F))%e / 3 6x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(a+b*(c+d*x))*(e+f*x)^2/x^5, x)
(71) 3 3 2 3 3 2 2 3 2 2 2 2 2 - b d e x log(F) + (- 8b d e f x - b d e x )log(F) + 2 3 2 2 2 2 2 (- 12b d f x - 8b d e f x - 2b d e x)log(F) - 12f x - 16e f x - 6e * (b d x + b c + a)log(F) %e + 4 4 2 4 4 3 3 4 3 2 2 2 4 2 (b d e x log(F) + 8b d e f x log(F) + 12b d f x log(F) ) * (b c + a)log(F) Ei(b d x log(F))%e / 4 24x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
-- Integrands of the form (c+d x)^m (a+b x)^n F^(e (a+b x)) integrate(%e^(-a-b*x)*(a+b*x)^4*(c+d*x)^3, x)
(72) 7 3 7 6 3 7 2 6 - b d x + ((- 4a - 7)b d - 3b c d )x + 2 5 3 6 2 7 2 5 ((- 6a - 24a - 42)b d + (- 12a - 18)b c d - 3b c d)x + 3 2 4 3 2 5 2 (- 4a - 30a - 120a - 210)b d + (- 18a - 60a - 90)b c d + 6 2 7 3 (- 12a - 15)b c d - b c * 4 x + 4 3 2 3 3 (- a - 16a - 120a - 480a - 840)b d + 3 2 4 2 2 5 2 (- 12a - 72a - 240a - 360)b c d + (- 18a - 48a - 60)b c d + 6 3 (- 4a - 4)b c * 3 x + 4 3 2 2 3 (- 3a - 48a - 360a - 1440a - 2520)b d + 4 3 2 3 2 (- 3a - 36a - 216a - 720a - 1080)b c d + 3 2 4 2 2 5 3 (- 12a - 54a - 144a - 180)b c d + (- 6a - 12a - 12)b c * 2 x + 4 3 2 3 (- 6a - 96a - 720a - 2880a - 5040)b d + 4 3 2 2 2 (- 6a - 72a - 432a - 1440a - 2160)b c d + 4 3 2 3 2 (- 3a - 24a - 108a - 288a - 360)b c d + 3 2 4 3 (- 4a - 12a - 24a - 24)b c * x + 4 3 2 3 (- 6a - 96a - 720a - 2880a - 5040)d + 4 3 2 2 (- 6a - 72a - 432a - 1440a - 2160)b c d + 4 3 2 2 2 (- 3a - 24a - 108a - 288a - 360)b c d + 4 3 2 3 3 (- a - 4a - 12a - 24a - 24)b c * - b x - a %e / 4 b
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(%e^(-a-b*x)*(a+b*x)^4*(c+d*x)^2, x)
(73) 6 2 6 5 2 6 5 - b d x + ((- 4a - 6)b d - 2b c d)x + 2 4 2 5 6 2 4 ((- 6a - 20a - 30)b d + (- 8a - 10)b c d - b c )x + 3 2 3 2 2 4 (- 4a - 24a - 80a - 120)b d + (- 12a - 32a - 40)b c d + 5 2 (- 4a - 4)b c * 3 x + 4 3 2 2 2 (- a - 12a - 72a - 240a - 360)b d + 3 2 3 2 4 2 (- 8a - 36a - 96a - 120)b c d + (- 6a - 12a - 12)b c * 2 x + 4 3 2 2 (- 2a - 24a - 144a - 480a - 720)b d + 4 3 2 2 (- 2a - 16a - 72a - 192a - 240)b c d + 3 2 3 2 (- 4a - 12a - 24a - 24)b c * x + 4 3 2 2 (- 2a - 24a - 144a - 480a - 720)d + 4 3 2 (- 2a - 16a - 72a - 192a - 240)b c d + 4 3 2 2 2 (- a - 4a - 12a - 24a - 24)b c * - b x - a %e / 3 b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^4*(c+d*x), x)
(74) 5 5 4 5 4 - b d x + ((- 4a - 5)b d - b c)x + 2 3 4 3 ((- 6a - 16a - 20)b d + (- 4a - 4)b c)x + 3 2 2 2 3 2 ((- 4a - 18a - 48a - 60)b d + (- 6a - 12a - 12)b c)x + 4 3 2 3 2 2 ((- a - 8a - 36a - 96a - 120)b d + (- 4a - 12a - 24a - 24)b c)x + 4 3 2 4 3 2 (- a - 8a - 36a - 96a - 120)d + (- a - 4a - 12a - 24a - 24)b c * - b x - a %e / 2 b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^4, x)
(75) 4 4 3 3 2 2 2 - b x + (- 4a - 4)b x + (- 6a - 12a - 12)b x + 3 2 4 3 2 (- 4a - 12a - 24a - 24)b x - a - 4a - 12a - 24a - 24 * - b x - a %e / b
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x), x)
(76) 4 4 3 3 2 2 2 2 3 3 4 4 - b d x - b c (a d - 4a b c d + 6a b c d - 4a b c d + b c )Ei(-------------) d * - a d + b c ----------- d %e + 3 4 3 2 4 3 3 2 - b d x + ((- 4a - 3)b d + b c d )x + 2 4 2 3 3 2 2 ((- 6a - 8a - 6)b d + (4a + 2)b c d - b c d )x + 3 2 4 2 3 2 2 2 (- 4a - 6a - 8a - 6)d + (6a + 4a + 2)b c d + (- 4a - 1)b c d + 3 3 b c d * - b x - a %e / 5 d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^2, x)
(77) 4 3 5 3 2 2 4 2 3 2 3 (- a + 4a )b d + (4a - 12a )b c d + (- 6a + 12a)b c d + 4 3 2 5 4 (4a - 4)b c d - b c d * x + 4 3 4 3 2 2 2 3 2 3 3 2 (- a + 4a )b c d + (4a - 12a )b c d + (- 6a + 12a)b c d + 4 4 5 5 (4a - 4)b c d - b c * - a d + b c ----------- - b d x - b c d Ei(-------------)%e d + 3 5 3 2 5 3 4 2 - b d x + ((- 4a - 2)b d + b c d )x + 2 5 2 4 3 2 3 4 5 ((- 6a - 4a - 2)b d + 4a b c d - b c d )x - a d + 3 2 4 2 2 2 3 3 3 2 (4a - 6a - 4a - 2)b c d + (- 6a + 8a + 2)b c d + (4a - 3)b c d + 4 4 - b c d * - b x - a %e / 7 6 d x + c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^3, x)
(78) 4 3 2 2 6 3 2 3 5 (a - 8a + 12a )b d + (- 4a + 24a - 24a)b c d + 2 4 2 4 5 3 3 6 4 2 (6a - 24a + 12)b c d + (- 4a + 8)b c d + b c d * 2 x + 4 3 2 2 5 3 2 3 2 4 (2a - 16a + 24a )b c d + (- 8a + 48a - 48a)b c d + 2 4 3 3 5 4 2 6 5 (12a - 48a + 24)b c d + (- 8a + 16)b c d + 2b c d * x + 4 3 2 2 2 4 3 2 3 3 3 (a - 8a + 12a )b c d + (- 4a + 24a - 24a)b c d + 2 4 4 2 5 5 6 6 (6a - 24a + 12)b c d + (- 4a + 8)b c d + b c * - a d + b c ----------- - b d x - b c d Ei(-------------)%e d + 3 6 3 2 6 3 5 2 - 2b d x + ((- 8a - 2)b d + 2b c d )x + 4 3 6 3 2 2 5 (a - 8a )b d + (- 4a + 24a - 16a - 4)b c d + 2 3 2 4 4 3 3 5 4 2 (6a - 24a + 10)b c d + (- 4a + 8)b c d + b c d * x + 4 6 4 3 5 3 2 2 2 4 - a d + (a - 4a )b c d + (- 4a + 18a - 8a - 2)b c d + 2 3 3 3 4 4 2 5 5 (6a - 20a + 6)b c d + (- 4a + 7)b c d + b c d * - b x - a %e / 9 2 8 2 7 2d x + 4c d x + 2c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) + 0.01 (OT) = 0.03 sec
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^4, x)
(79) 4 3 2 3 7 3 2 4 6 (- a + 12a - 36a + 24a)b d + (4a - 36a + 72a - 24)b c d + 2 5 2 5 6 3 4 7 4 3 (- 6a + 36a - 36)b c d + (4a - 12)b c d - b c d * 3 x + 4 3 2 3 6 (- 3a + 36a - 108a + 72a)b c d + 3 2 4 2 5 2 5 3 4 (12a - 108a + 216a - 72)b c d + (- 18a + 108a - 108)b c d + 6 4 3 7 5 2 (12a - 36)b c d - 3b c d * 2 x + 4 3 2 3 2 5 (- 3a + 36a - 108a + 72a)b c d + 3 2 4 3 4 2 5 4 3 (12a - 108a + 216a - 72)b c d + (- 18a + 108a - 108)b c d + 6 5 2 7 6 (12a - 36)b c d - 3b c d * x + 4 3 2 3 3 4 3 2 4 4 3 (- a + 12a - 36a + 24a)b c d + (4a - 36a + 72a - 24)b c d + 2 5 5 2 6 6 7 7 (- 6a + 36a - 36)b c d + (4a - 12)b c d - b c * - a d + b c ----------- - b d x - b c d Ei(-------------)%e d + 3 7 3 - 6b d x + 4 3 2 2 7 3 2 3 6 (- a + 12a - 36a )b d + (4a - 36a + 72a - 18)b c d + 2 4 2 5 5 3 4 6 4 3 (- 6a + 36a - 36)b c d + (4a - 12)b c d - b c d * 2 x + 4 3 7 4 3 2 2 6 (a - 12a )b d + (- 2a + 20a - 36a )b c d + 3 2 3 2 5 2 4 3 4 (8a - 66a + 108a - 18)b c d + (- 12a + 68a - 60)b c d + 5 4 3 6 5 2 (8a - 23)b c d - 2b c d * x + 4 7 4 3 6 4 3 2 2 2 5 - 2a d + (a - 4a )b c d + (- a + 8a - 12a )b c d + 3 2 3 3 4 2 4 4 3 (4a - 30a + 44a - 6)b c d + (- 6a + 32a - 26)b c d + 5 5 2 6 6 (4a - 11)b c d - b c d * - b x - a %e / 11 3 10 2 2 9 3 8 6d x + 18c d x + 18c d x + 6c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(%e^(-a-b*x)*(a+b*x)^4/(c+d*x)^5, x)
(80) 4 3 2 4 8 (a - 16a + 72a - 96a + 24)b d + 3 2 5 7 2 6 2 6 (- 4a + 48a - 144a + 96)b c d + (6a - 48a + 72)b c d + 7 3 5 8 4 4 (- 4a + 16)b c d + b c d * 4 x + 4 3 2 4 7 (4a - 64a + 288a - 384a + 96)b c d + 3 2 5 2 6 2 6 3 5 (- 16a + 192a - 576a + 384)b c d + (24a - 192a + 288)b c d + 7 4 4 8 5 3 (- 16a + 64)b c d + 4b c d * 3 x + 4 3 2 4 2 6 (6a - 96a + 432a - 576a + 144)b c d + 3 2 5 3 5 2 6 4 4 (- 24a + 288a - 864a + 576)b c d + (36a - 288a + 432)b c d + 7 5 3 8 6 2 (- 24a + 96)b c d + 6b c d * 2 x + 4 3 2 4 3 5 (4a - 64a + 288a - 384a + 96)b c d + 3 2 5 4 4 2 6 5 3 (- 16a + 192a - 576a + 384)b c d + (24a - 192a + 288)b c d + 7 6 2 8 7 (- 16a + 64)b c d + 4b c d * x + 4 3 2 4 4 4 (a - 16a + 72a - 96a + 24)b c d + 3 2 5 5 3 2 6 6 2 (- 4a + 48a - 144a + 96)b c d + (6a - 48a + 72)b c d + 7 7 8 8 (- 4a + 16)b c d + b c * - a d + b c ----------- - b d x - b c d Ei(-------------)%e d + 4 3 2 3 8 3 2 4 7 (a - 16a + 72a - 96a)b d + (- 4a + 48a - 144a + 96)b c d + 2 5 2 6 6 3 5 7 4 4 (6a - 48a + 72)b c d + (- 4a + 16)b c d + b c d * 3 x + 4 3 2 2 8 4 3 2 3 7 (- a + 16a - 72a )b d + (3a - 44a + 168a - 144a)b c d + 3 2 4 2 6 2 5 3 5 (- 12a + 138a - 384a + 216)b c d + (18a - 140a + 200)b c d + 6 4 4 7 5 3 (- 12a + 47)b c d + 3b c d * 2 x + 4 3 8 4 3 2 2 7 (2a - 32a )b d + (- 2a + 24a - 48a )b c d + 4 3 2 3 2 6 (3a - 40a + 132a - 96a)b c d + 3 2 4 3 5 2 5 4 4 (- 12a + 132a - 344a + 176)b c d + (18a - 136a + 186)b c d + 6 5 3 7 6 2 (- 12a + 46)b c d + 3b c d * x + 4 8 4 3 7 4 3 2 2 2 6 - 6a d + (2a - 8a )b c d + (- a + 8a - 12a )b c d + 4 3 2 3 3 5 3 2 4 4 4 (a - 12a + 36a - 24a)b c d + (- 4a + 42a - 104a + 50)b c d + 2 5 5 3 6 6 2 7 7 (6a - 44a + 58)b c d + (- 4a + 15)b c d + b c d * - b x - a %e / 13 4 12 3 2 11 2 3 10 4 9 24d x + 96c d x + 144c d x + 96c d x + 24c d
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) + 0.01 (OT) = 0.04 sec
-- Integrands of the form x^m F(c (a+b x)) Logintegrate(d x] (e+(f+g x) Log[d x]) integrate(F^(c*(a+b*x))*x^m*log(d*x)^n*(e+e*n+e*(1+m+b*c*x*log(F))*log(d*x)), x)
(81) (b c x + a c)log(F) m log(x) (e x log(x) + e x log(d))%e %e * n log(log(x) + log(d)) %e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(F^(c*(a+b*x))*x^2*log(d*x)^n*(e+e*n+e*(3+b*c*x*log(F))*log(d*x)), x)
3 (b c x + a c)log(F) n log(log(d x)) (82) e x log(d x)%e %e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*x*log(d*x)^n*(e+e*n+e*(2+b*c*x*log(F))*log(d*x)), x)
2 (b c x + a c)log(F) n log(log(d x)) (83) e x log(d x)%e %e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+e*(1+b*c*x*log(F))*log(d*x)), x)
(b c x + a c)log(F) n log(log(d x)) (84) e x log(d x)%e %e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+b*c*e*x*log(F)*log(d*x))/x, x)
(b c x + a c)log(F) n log(log(d x)) (85) e log(d x)%e %e
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+e*(-1+b*c*x*log(F))*log(d*x))/x^2, x)
(b c x + a c)log(F) n log(log(d x)) e log(d x)%e %e (86) ------------------------------------------------ x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(F^(c*(a+b*x))*log(d*x)^n*(e+e*n+e*(-2+b*c*x*log(F))*log(d*x))/x^3, x)
(b c x + a c)log(F) n log(log(d x)) e log(d x)%e %e (87) ------------------------------------------------ 2 x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
-- Integrands of the form x^m F^(a+b x^n)
-- n>0 integrate(f^(a+b*x^2)*x^m, x)
x 2 ++ m %A b + a (88) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^11, x)
(89) 5 10 5 4 8 4 3 6 3 2 4 2 b x log(f) - 5b x log(f) + 20b x log(f) - 60b x log(f) + 2 120b x log(f) - 120 * 2 (b x + a)log(f) %e / 6 6 2b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^2)*x^9, x)
(90) 4 8 4 3 6 3 2 4 2 2 (b x log(f) - 4b x log(f) + 12b x log(f) - 24b x log(f) + 24) * 2 (b x + a)log(f) %e / 5 5 2b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^7, x)
2 3 6 3 2 4 2 2 (b x + a)log(f) (b x log(f) - 3b x log(f) + 6b x log(f) - 6)%e (91) ---------------------------------------------------------------- 4 4 2b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(a+b*x^2)*x^5, x)
2 2 4 2 2 (b x + a)log(f) (b x log(f) - 2b x log(f) + 2)%e (92) ------------------------------------------------- 3 3 2b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^3, x)
2 2 (b x + a)log(f) (b x log(f) - 1)%e (93) ---------------------------------- 2 2 2b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x, x)
2 (b x + a)log(f) %e (94) ------------------ 2b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x, x)
2 a log(f) Ei(b x log(f))%e (95) ------------------------ 2
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^2)/x^3, x)
2 (b x + a)log(f) 2 2 a log(f) - %e + b x log(f)Ei(b x log(f))%e (96) --------------------------------------------------------- 2 2x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^5, x)
(97) 2 2 (b x + a)log(f) 2 4 2 2 a log(f) (- b x log(f) - 1)%e + b x log(f) Ei(b x log(f))%e -------------------------------------------------------------------------- 4 4x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^7, x)
(98) 2 2 4 2 2 (b x + a)log(f) (- b x log(f) - b x log(f) - 2)%e + 3 6 3 2 a log(f) b x log(f) Ei(b x log(f))%e / 6 12x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^2)/x^9, x)
(99) 2 3 6 3 2 4 2 2 (b x + a)log(f) (- b x log(f) - b x log(f) - 2b x log(f) - 6)%e + 4 8 4 2 a log(f) b x log(f) Ei(b x log(f))%e / 8 48x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^11, x)
(100) 4 8 4 3 6 3 2 4 2 2 (- b x log(f) - b x log(f) - 2b x log(f) - 6b x log(f) - 24) * 2 (b x + a)log(f) %e + 5 10 5 2 a log(f) b x log(f) Ei(b x log(f))%e / 10 240x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^12, x)
(101) +---+ a log(f) +----------+ 10395\|%pi %e erf(x\|- b log(f) ) + 5 11 5 4 9 4 3 7 3 2 5 2 64b x log(f) - 352b x log(f) + 1584b x log(f) - 5544b x log(f) + 3 13860b x log(f) - 20790x * 2 (b x + a)log(f) +----------+ %e \|- b log(f) / 6 6 +----------+ 128b log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^2)*x^10, x)
(102) +---+ a log(f) +----------+ - 945\|%pi %e erf(x\|- b log(f) ) + 4 9 4 3 7 3 2 5 2 3 32b x log(f) - 144b x log(f) + 504b x log(f) - 1260b x log(f) + 1890x * 2 (b x + a)log(f) +----------+ %e \|- b log(f) / 5 5 +----------+ 64b log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^2)*x^8, x)
(103) +---+ a log(f) +----------+ 105\|%pi %e erf(x\|- b log(f) ) + 3 7 3 2 5 2 3 (16b x log(f) - 56b x log(f) + 140b x log(f) - 210x) * 2 (b x + a)log(f) +----------+ %e \|- b log(f) / 4 4 +----------+ 32b log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^6, x)
(104) +---+ a log(f) +----------+ - 15\|%pi %e erf(x\|- b log(f) ) + 2 2 5 2 3 (b x + a)log(f) +----------+ (8b x log(f) - 20b x log(f) + 30x)%e \|- b log(f) / 3 3 +----------+ 16b log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^2)*x^4, x)
(105) +---+ a log(f) +----------+ 3\|%pi %e erf(x\|- b log(f) ) + 2 3 (b x + a)log(f) +----------+ (4b x log(f) - 6x)%e \|- b log(f) / 2 2 +----------+ 8b log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)*x^2, x)
(106) 2 +---+ a log(f) +----------+ (b x + a)log(f) +----------+ - \|%pi %e erf(x\|- b log(f) ) + 2x %e \|- b log(f) -------------------------------------------------------------------------- +----------+ 4b log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2), x)
+---+ a log(f) +----------+ \|%pi %e erf(x\|- b log(f) ) (107) ----------------------------------- +----------+ 2\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(a+b*x^2)/x^2, x)
(108) +---+ a log(f) +----------+ b x log(f)\|%pi %e erf(x\|- b log(f) ) + 2 (b x + a)log(f) +----------+ - %e \|- b log(f) / +----------+ x\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^4, x)
(109) 2 3 2 +---+ a log(f) +----------+ 2b x log(f) \|%pi %e erf(x\|- b log(f) ) + 2 2 (b x + a)log(f) +----------+ (- 2b x log(f) - 1)%e \|- b log(f) / 3 +----------+ 3x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^2)/x^6, x)
(110) 3 5 3 +---+ a log(f) +----------+ 4b x log(f) \|%pi %e erf(x\|- b log(f) ) + 2 2 4 2 2 (b x + a)log(f) +----------+ (- 4b x log(f) - 2b x log(f) - 3)%e \|- b log(f) / 5 +----------+ 15x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^8, x)
(111) 4 7 4 +---+ a log(f) +----------+ 8b x log(f) \|%pi %e erf(x\|- b log(f) ) + 2 3 6 3 2 4 2 2 (b x + a)log(f) (- 8b x log(f) - 4b x log(f) - 6b x log(f) - 15)%e * +----------+ \|- b log(f) / 7 +----------+ 105x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^10, x)
(112) 5 9 5 +---+ a log(f) +----------+ 16b x log(f) \|%pi %e erf(x\|- b log(f) ) + 4 8 4 3 6 3 2 4 2 2 (- 16b x log(f) - 8b x log(f) - 12b x log(f) - 30b x log(f) - 105) * 2 (b x + a)log(f) +----------+ %e \|- b log(f) / 9 +----------+ 945x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^2)/x^12, x)
(113) 6 11 6 +---+ a log(f) +----------+ 32b x log(f) \|%pi %e erf(x\|- b log(f) ) + 5 10 5 4 8 4 3 6 3 2 4 2 - 32b x log(f) - 16b x log(f) - 24b x log(f) - 60b x log(f) + 2 - 210b x log(f) - 945 * 2 (b x + a)log(f) +----------+ %e \|- b log(f) / 11 +----------+ 10395x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^3)*x^m, x)
x 3 ++ m %A b + a (114) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^17, x)
(115) 5 15 5 4 12 4 3 9 3 2 6 2 b x log(f) - 5b x log(f) + 20b x log(f) - 60b x log(f) + 3 120b x log(f) - 120 * 3 (b x + a)log(f) %e / 6 6 3b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^3)*x^14, x)
(116) 4 12 4 3 9 3 2 6 2 3 (b x log(f) - 4b x log(f) + 12b x log(f) - 24b x log(f) + 24) * 3 (b x + a)log(f) %e / 5 5 3b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^11, x)
3 3 9 3 2 6 2 3 (b x + a)log(f) (b x log(f) - 3b x log(f) + 6b x log(f) - 6)%e (117) ---------------------------------------------------------------- 4 4 3b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(a+b*x^3)*x^8, x)
3 2 6 2 3 (b x + a)log(f) (b x log(f) - 2b x log(f) + 2)%e (118) ------------------------------------------------- 3 3 3b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^5, x)
3 3 (b x + a)log(f) (b x log(f) - 1)%e (119) ---------------------------------- 2 2 3b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(a+b*x^3)*x^2, x)
3 (b x + a)log(f) %e (120) ------------------ 3b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x, x)
3 a log(f) Ei(b x log(f))%e (121) ------------------------ 3
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x^4, x)
3 (b x + a)log(f) 3 3 a log(f) - %e + b x log(f)Ei(b x log(f))%e (122) --------------------------------------------------------- 3 3x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x^7, x)
(123) 3 3 (b x + a)log(f) 2 6 2 3 a log(f) (- b x log(f) - 1)%e + b x log(f) Ei(b x log(f))%e -------------------------------------------------------------------------- 6 6x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x^10, x)
(124) 3 2 6 2 3 (b x + a)log(f) (- b x log(f) - b x log(f) - 2)%e + 3 9 3 3 a log(f) b x log(f) Ei(b x log(f))%e / 9 18x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x^13, x)
(125) 3 3 9 3 2 6 2 3 (b x + a)log(f) (- b x log(f) - b x log(f) - 2b x log(f) - 6)%e + 4 12 4 3 a log(f) b x log(f) Ei(b x log(f))%e / 12 72x
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^3)/x^16, x)
(126) 4 12 4 3 9 3 2 6 2 3 (- b x log(f) - b x log(f) - 2b x log(f) - 6b x log(f) - 24) * 3 (b x + a)log(f) %e + 5 15 5 3 a log(f) b x log(f) Ei(b x log(f))%e / 15 360x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x^4, x)
(127) 3 2 (b x + a)log(f) 3+----------+2 a log(f) 2 3 3x %e \|- b log(f) + 2%e Gamma(-,- b x log(f)) 3 ---------------------------------------------------------------------- 3+----------+2 9b log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^3)*x^3, x)
3 (b x + a)log(f) 3+----------+ a log(f) 1 3 3x %e \|- b log(f) + %e Gamma(-,- b x log(f)) 3 (128) -------------------------------------------------------------------- 3+----------+ 9b log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)*x, x)
a log(f) 2 3 %e Gamma(-,- b x log(f)) 3 (129) - ------------------------------- 3+----------+2 3\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3), x)
a log(f) 1 3 %e Gamma(-,- b x log(f)) 3 (130) - ------------------------------- 3+----------+ 3\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(a+b*x^3)/x^2, x)
(131) 3 (b x + a)log(f) 3+----------+2 - %e \|- b log(f) + a log(f) 2 3 - b x log(f)%e Gamma(-,- b x log(f)) 3 / 3+----------+2 x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^3)/x^3, x)
(132) 3 (b x + a)log(f) 3+----------+ 2 a log(f) 1 3 - %e \|- b log(f) - b x log(f)%e Gamma(-,- b x log(f)) 3 ----------------------------------------------------------------------------- 2 3+----------+ 2x \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(%e^(4*x^3)*x^2, x)
3 4x %e (133) ----- 12
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- n<0 integrate(f^(a+b/x)*x^m, x)
b + %A a x -------- ++ m %A (134) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x)*x^4, x)
(135) 4 4 3 2 3 2 3 2 4 5 (b x log(f) + b x log(f) + 2b x log(f) + 6b x log(f) + 24x ) * (a x + b)log(f) --------------- x %e + 5 5 b log(f) a log(f) - b log(f) Ei(--------)%e x / 120
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)*x^3, x)
(136) (a x + b)log(f) --------------- 3 3 2 2 2 3 4 x (b x log(f) + b x log(f) + 2b x log(f) + 6x )%e + 4 4 b log(f) a log(f) - b log(f) Ei(--------)%e x / 24
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x)*x^2, x)
(137) (a x + b)log(f) --------------- 2 2 2 3 x (b x log(f) + b x log(f) + 2x )%e + 3 3 b log(f) a log(f) - b log(f) Ei(--------)%e x / 6
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)*x, x)
(a x + b)log(f) --------------- 2 x 2 2 b log(f) a log(f) (b x log(f) + x )%e - b log(f) Ei(--------)%e x (138) -------------------------------------------------------------------- 2
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x), x)
(a x + b)log(f) --------------- x b log(f) a log(f) (139) x %e - b log(f)Ei(--------)%e x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)/x, x)
b log(f) a log(f) (140) - Ei(--------)%e x
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)/x^2, x)
(a x + b)log(f) --------------- x %e (141) - ----------------- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)/x^3, x)
(a x + b)log(f) --------------- x (- b log(f) + x)%e (142) --------------------------------- 2 2 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(a+b/x)/x^4, x)
(a x + b)log(f) --------------- 2 2 2 x (- b log(f) + 2b x log(f) - 2x )%e (143) -------------------------------------------------- 3 2 3 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)/x^5, x)
(a x + b)log(f) --------------- 3 3 2 2 2 3 x (- b log(f) + 3b x log(f) - 6b x log(f) + 6x )%e (144) ----------------------------------------------------------------- 4 3 4 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)/x^6, x)
(145) 4 4 3 3 2 2 2 3 4 (- b log(f) + 4b x log(f) - 12b x log(f) + 24b x log(f) - 24x ) * (a x + b)log(f) --------------- x %e / 5 4 5 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x)/x^7, x)
(146) 5 5 4 4 3 2 3 2 3 2 - b log(f) + 5b x log(f) - 20b x log(f) + 60b x log(f) + 4 5 - 120b x log(f) + 120x * (a x + b)log(f) --------------- x %e / 6 5 6 b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)*x^m, x)
2 b + %A a -------- x 2 ++ m %A (147) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)*x^9, x)
(148) 4 2 4 3 4 3 2 6 2 8 10 (b x log(f) + b x log(f) + 2b x log(f) + 6b x log(f) + 24x ) * 2 (a x + b)log(f) ---------------- 2 x %e + 5 5 b log(f) a log(f) - b log(f) Ei(--------)%e 2 x / 240
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)*x^7, x)
(149) 2 (a x + b)log(f) ---------------- 2 3 2 3 2 4 2 6 8 x (b x log(f) + b x log(f) + 2b x log(f) + 6x )%e + 4 4 b log(f) a log(f) - b log(f) Ei(--------)%e 2 x / 48
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)*x^5, x)
(150) 2 (a x + b)log(f) ---------------- 2 2 2 2 4 6 x (b x log(f) + b x log(f) + 2x )%e + 3 3 b log(f) a log(f) - b log(f) Ei(--------)%e 2 x / 12
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(a+b/x^2)*x^3, x)
(151) 2 (a x + b)log(f) ---------------- 2 2 4 x 2 2 b log(f) a log(f) (b x log(f) + x )%e - b log(f) Ei(--------)%e 2 x --------------------------------------------------------------------- 4
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(a+b/x^2)*x, x)
2 (a x + b)log(f) ---------------- 2 2 x b log(f) a log(f) x %e - b log(f)Ei(--------)%e 2 x (152) ----------------------------------------------------- 2
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x, x)
b log(f) a log(f) Ei(--------)%e 2 x (153) - ---------------------- 2
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^3, x)
2 (a x + b)log(f) ---------------- 2 x %e (154) - ------------------ 2b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^5, x)
2 (a x + b)log(f) ---------------- 2 2 x (- b log(f) + x )%e (155) ----------------------------------- 2 2 2 2b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^7, x)
2 (a x + b)log(f) ---------------- 2 2 2 2 4 x (- b log(f) + 2b x log(f) - 2x )%e (156) --------------------------------------------------- 3 4 3 2b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^9, x)
2 (a x + b)log(f) ---------------- 2 3 3 2 2 2 4 6 x (- b log(f) + 3b x log(f) - 6b x log(f) + 6x )%e (157) ------------------------------------------------------------------ 4 6 4 2b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^11, x)
(158) 4 4 3 2 3 2 4 2 6 8 (- b log(f) + 4b x log(f) - 12b x log(f) + 24b x log(f) - 24x ) * 2 (a x + b)log(f) ---------------- 2 x %e / 5 8 5 2b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^13, x)
(159) 5 5 4 2 4 3 4 3 2 6 2 - b log(f) + 5b x log(f) - 20b x log(f) + 60b x log(f) + 8 10 - 120b x log(f) + 120x * 2 (a x + b)log(f) ---------------- 2 x %e / 6 10 6 2b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)*x^10, x)
(160) +----------+ 6 6 +---+ a log(f) \|- b log(f) - 32b log(f) \|%pi %e erf(-------------) x + 5 5 4 3 4 3 5 3 2 7 2 32b x log(f) + 16b x log(f) + 24b x log(f) + 60b x log(f) + 9 11 210b x log(f) + 945x * 2 (a x + b)log(f) ---------------- 2 x +----------+ %e \|- b log(f) / +----------+ 10395\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(a+b/x^2)*x^8, x)
(161) +----------+ 5 5 +---+ a log(f) \|- b log(f) - 16b log(f) \|%pi %e erf(-------------) x + 4 4 3 3 3 2 5 2 7 9 (16b x log(f) + 8b x log(f) + 12b x log(f) + 30b x log(f) + 105x ) * 2 (a x + b)log(f) ---------------- 2 x +----------+ %e \|- b log(f) / +----------+ 945\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)*x^6, x)
(162) +----------+ 4 4 +---+ a log(f) \|- b log(f) - 8b log(f) \|%pi %e erf(-------------) x + 2 (a x + b)log(f) ---------------- 2 3 3 2 3 2 5 7 x (8b x log(f) + 4b x log(f) + 6b x log(f) + 15x )%e * +----------+ \|- b log(f) / +----------+ 105\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)*x^4, x)
(163) +----------+ 3 3 +---+ a log(f) \|- b log(f) - 4b log(f) \|%pi %e erf(-------------) x + 2 (a x + b)log(f) ---------------- 2 2 2 3 5 x +----------+ (4b x log(f) + 2b x log(f) + 3x )%e \|- b log(f) / +----------+ 15\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)*x^2, x)
(164) +----------+ 2 2 +---+ a log(f) \|- b log(f) - 2b log(f) \|%pi %e erf(-------------) x + 2 (a x + b)log(f) ---------------- 2 3 x +----------+ (2b x log(f) + x )%e \|- b log(f) / +----------+ 3\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2), x)
(165) +----------+ +---+ a log(f) \|- b log(f) - b log(f)\|%pi %e erf(-------------) x + 2 (a x + b)log(f) ---------------- 2 x +----------+ x %e \|- b log(f) / +----------+ \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^2, x)
+----------+ +---+ a log(f) \|- b log(f) \|%pi %e erf(-------------) x (166) - ---------------------------------- +----------+ 2\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^4, x)
(167) 2 (a x + b)log(f) ---------------- +----------+ 2 +---+ a log(f) \|- b log(f) x +----------+ x\|%pi %e erf(-------------) - 2%e \|- b log(f) x ---------------------------------------------------------------------- +----------+ 4b x log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^6, x)
(168) +----------+ 3 +---+ a log(f) \|- b log(f) - 3x \|%pi %e erf(-------------) x + 2 (a x + b)log(f) ---------------- 2 2 x +----------+ (- 4b log(f) + 6x )%e \|- b log(f) / 2 3 2 +----------+ 8b x log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^8, x)
(169) +----------+ 5 +---+ a log(f) \|- b log(f) 15x \|%pi %e erf(-------------) x + 2 (a x + b)log(f) ---------------- 2 2 2 2 4 x +----------+ (- 8b log(f) + 20b x log(f) - 30x )%e \|- b log(f) / 3 5 3 +----------+ 16b x log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^2)/x^10, x)
(170) +----------+ 7 +---+ a log(f) \|- b log(f) - 105x \|%pi %e erf(-------------) x + 3 3 2 2 2 4 6 (- 16b log(f) + 56b x log(f) - 140b x log(f) + 210x ) * 2 (a x + b)log(f) ---------------- 2 x +----------+ %e \|- b log(f) / 4 7 4 +----------+ 32b x log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^12, x)
(171) +----------+ 9 +---+ a log(f) \|- b log(f) 945x \|%pi %e erf(-------------) x + 4 4 3 2 3 2 4 2 6 - 32b log(f) + 144b x log(f) - 504b x log(f) + 1260b x log(f) + 8 - 1890x * 2 (a x + b)log(f) ---------------- 2 x +----------+ %e \|- b log(f) / 5 9 5 +----------+ 64b x log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^2)/x^14, x)
(172) +----------+ 11 +---+ a log(f) \|- b log(f) - 10395x \|%pi %e erf(-------------) x + 5 5 4 2 4 3 4 3 2 6 2 - 64b log(f) + 352b x log(f) - 1584b x log(f) + 5544b x log(f) + 8 10 - 13860b x log(f) + 20790x * 2 (a x + b)log(f) ---------------- 2 x +----------+ %e \|- b log(f) / 6 11 6 +----------+ 128b x log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)*x^m, x)
3 b + %A a -------- x 3 ++ m %A (173) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)*x^14, x)
(174) 4 3 4 3 6 3 2 9 2 12 15 (b x log(f) + b x log(f) + 2b x log(f) + 6b x log(f) + 24x ) * 3 (a x + b)log(f) ---------------- 3 x %e + 5 5 b log(f) a log(f) - b log(f) Ei(--------)%e 3 x / 360
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)*x^11, x)
(175) 3 (a x + b)log(f) ---------------- 3 3 3 3 2 6 2 9 12 x (b x log(f) + b x log(f) + 2b x log(f) + 6x )%e + 4 4 b log(f) a log(f) - b log(f) Ei(--------)%e 3 x / 72
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(a+b/x^3)*x^8, x)
(176) 3 (a x + b)log(f) ---------------- 3 2 3 2 6 9 x (b x log(f) + b x log(f) + 2x )%e + 3 3 b log(f) a log(f) - b log(f) Ei(--------)%e 3 x / 18
Type: Union(Expression(Integer),...)
fricas
Time: 0.02 (EV) = 0.02 sec
integrate(f^(a+b/x^3)*x^5, x)
(177) 3 (a x + b)log(f) ---------------- 3 3 6 x 2 2 b log(f) a log(f) (b x log(f) + x )%e - b log(f) Ei(--------)%e 3 x --------------------------------------------------------------------- 6
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)*x^2, x)
3 (a x + b)log(f) ---------------- 3 3 x b log(f) a log(f) x %e - b log(f)Ei(--------)%e 3 x (178) ----------------------------------------------------- 3
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x, x)
b log(f) a log(f) Ei(--------)%e 3 x (179) - ---------------------- 3
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x^4, x)
3 (a x + b)log(f) ---------------- 3 x %e (180) - ------------------ 3b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(a+b/x^3)/x^7, x)
3 (a x + b)log(f) ---------------- 3 3 x (- b log(f) + x )%e (181) ----------------------------------- 2 3 2 3b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x^10, x)
3 (a x + b)log(f) ---------------- 3 2 2 3 6 x (- b log(f) + 2b x log(f) - 2x )%e (182) --------------------------------------------------- 3 6 3 3b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)/x^13, x)
3 (a x + b)log(f) ---------------- 3 3 3 2 3 2 6 9 x (- b log(f) + 3b x log(f) - 6b x log(f) + 6x )%e (183) ------------------------------------------------------------------ 4 9 4 3b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x^16, x)
(184) 4 4 3 3 3 2 6 2 9 12 (- b log(f) + 4b x log(f) - 12b x log(f) + 24b x log(f) - 24x ) * 3 (a x + b)log(f) ---------------- 3 x %e / 5 12 5 3b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(a+b/x^3)/x^19, x)
(185) 5 5 4 3 4 3 6 3 2 9 2 - b log(f) + 5b x log(f) - 20b x log(f) + 60b x log(f) + 12 15 - 120b x log(f) + 120x * 3 (a x + b)log(f) ---------------- 3 x %e / 6 15 6 3b x log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)*x^4, x)
(186) 3 (a x + b)log(f) ---------------- 3 2 5 x 3+----------+ (3b x log(f) + 2x )%e \|- b log(f) + 2 2 a log(f) 1 b log(f) 3b log(f) %e Gamma(-,- --------) 3 3 x / 3+----------+ 10\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b/x^3)*x^3, x)
(187) 3 (a x + b)log(f) ---------------- 3 4 x 3+----------+2 (3b x log(f) + x )%e \|- b log(f) + 2 2 a log(f) 2 b log(f) 3b log(f) %e Gamma(-,- --------) 3 3 x / 3+----------+2 4\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)*x, x)
(188) 3 (a x + b)log(f) ---------------- 3 2 x 3+----------+ a log(f) 1 b log(f) x %e \|- b log(f) + b log(f)%e Gamma(-,- --------) 3 3 x ------------------------------------------------------------------------- 3+----------+ 2\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(a+b/x^3), x)
(189) 3 (a x + b)log(f) ---------------- 3 x 3+----------+2 a log(f) 2 b log(f) x %e \|- b log(f) + b log(f)%e Gamma(-,- --------) 3 3 x -------------------------------------------------------------------------- 3+----------+2 \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x^2, x)
a log(f) 1 b log(f) %e Gamma(-,- --------) 3 3 x (190) ----------------------------- 3+----------+ 3\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b/x^3)/x^3, x)
a log(f) 2 b log(f) %e Gamma(-,- --------) 3 3 x (191) ----------------------------- 3+----------+2 3\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (OT) = 0.01 sec
integrate(f^(a+b/x^3)/x^5, x)
3 (a x + b)log(f) ---------------- 3 x 3+----------+ a log(f) 1 b log(f) - 3%e \|- b log(f) - x %e Gamma(-,- --------) 3 3 x (192) -------------------------------------------------------------------- 3+----------+ 9b x log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
-- n symbolic integrate(f^(a+b*x^n)*x^m, x)
x n ++ m b %A + a (193) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)*x^3, x)
x n ++ 3 b %A + a (194) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)*x^2, x)
x n ++ 2 b %A + a (195) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)*x, x)
x n ++ b %A + a (196) | %A f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(a+b*x^n), x)
x n ++ b %A + a (197) | f d%A ++
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)/x, x)
a log(f) n log(x) %e Ei(b log(f)%e ) (198) -------------------------------- n
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)/x^2, x)
n x b %A + a ++ f (199) | ---------- d%A ++ 2 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)/x^3, x)
n x b %A + a ++ f (200) | ---------- d%A ++ 3 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)/x^4, x)
n x b %A + a ++ f (201) | ---------- d%A ++ 4 %A
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)*x^(-1+3*n), x)
(202) 2 2 n log(x) 2 n log(x) (b log(f) (%e ) - 2b log(f)%e + 2) * n log(x) b log(f)%e + a log(f) %e / 3 3 b n log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)*x^(-1+2*n), x)
n log(x) n log(x) b log(f)%e + a log(f) (b log(f)%e - 1)%e (203) ------------------------------------------------------- 2 2 b n log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)*x^(-1+n), x)
n log(x) b log(f)%e + a log(f) %e (204) ------------------------------- b n log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)/x, x)
a log(f) n log(x) %e Ei(b log(f)%e ) (205) -------------------------------- n
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (IN) = 0.01 sec
integrate(f^(a+b*x^n)*x^(-1-n), x)
(206) n log(x) b log(f)%e + a log(f) - %e + a log(f) n log(x) n log(x) b log(f)%e %e Ei(b log(f)%e ) / n log(x) n %e
Type: Union(Expression(Integer),...)
fricas
Time: 0 sec
integrate(f^(a+b*x^n)*x^(-1-2*n), x)
(207) n log(x) n log(x) b log(f)%e + a log(f) (- b log(f)%e - 1)%e + 2 2 a log(f) n log(x) 2 n log(x) b log(f) %e (%e ) Ei(b log(f)%e ) / n log(x) 2 2n (%e )
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)*x^(-1+5/2*n), x)
(208) n log(x) 3 n log(x) -------- -------- 2 2 +----------+ (4b log(f)(%e ) - 6%e )\|- b log(f) * n log(x) 2 -------- 2 b log(f)(%e ) + a log(f) %e + n log(x) -------- +---+ a log(f) 2 +----------+ 3\|%pi %e erf(%e \|- b log(f) ) / 2 2 +----------+ 4b n log(f) \|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
integrate(f^(a+b*x^n)*x^(-1+3/2*n), x)
(209) n log(x) 2 n log(x) -------- -------- 2 2 +----------+ b log(f)(%e ) + a log(f) 2%e \|- b log(f) %e + n log(x) -------- +---+ a log(f) 2 +----------+ - \|%pi %e erf(%e \|- b log(f) ) / +----------+ 2b n log(f)\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)*x^(-1+1/2*n), x)
(n - 2)log(x) ------------- +---+ a log(f) 2 +----------+ \|%pi %e erf(x %e \|- b log(f) ) (210) --------------------------------------------------- +----------+ n\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)*x^(-1-1/2*n), x)
(211) - (- n - 2)log(x) --------------- 2 +----------+ 2x %e \|- b log(f) * (- n - 2)log(x) 2 --------------- 2 2 a x log(f)(%e ) + b log(f) ----------------------------------------- (- n - 2)log(x) 2 --------------- 2 2 x (%e ) %e + +----------+ +---+ a log(f) \|- b log(f) 2b log(f)\|%pi %e erf(-------------------) (- n - 2)log(x) --------------- 2 x %e / +----------+ n\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.01 (EV) = 0.01 sec
integrate(f^(a+b*x^n)*x^(-1-3/2*n), x)
(212) (- 3n - 2)log(x) 3 (- 3n - 2)log(x) ---------------- ---------------- 6 3+-+ 6 (- 2x (%e ) - 4b log(f)\|x %e ) * (- 3n - 2)log(x) 2 ---------------- 3+-+2 6 a log(f)\|x (%e ) + b log(f) --------------------------------------------- (- 3n - 2)log(x) 2 ---------------- 3+-+2 6 +----------+ \|x (%e ) \|- b log(f) %e + +----------+ 2 2 +---+ a log(f) \|- b log(f) 4b log(f) \|%pi %e erf(----------------------) (- 3n - 2)log(x) ---------------- 3+-+ 6 \|x %e / +----------+ 3n\|- b log(f)
Type: Union(Expression(Integer),...)
fricas
Time: 0.03 (EV) = 0.03 sec
integrate(%e^((-0.1)*x)*x, x)
There are 12 exposed and 10 unexposed library operations named integrate having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op integrate to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation.
Cannot find a definition or applicable library operation named integrate with argument type(s) Expression(Float) Variable(x)
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.
Continuing to read the file...




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