3.39 \(\int \left (a+b \left (F^{g (e+f x)}\right )^n\right )^3 (c+d x)^3 \, dx\)

Optimal. Leaf size=496 \[ \frac{a^3 (c+d x)^4}{4 d}+\frac{18 a^2 b d^2 (c+d x) \left (F^{e g+f g x}\right )^n}{f^3 g^3 n^3 \log ^3(F)}-\frac{9 a^2 b d (c+d x)^2 \left (F^{e g+f g x}\right )^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{3 a^2 b (c+d x)^3 \left (F^{e g+f g x}\right )^n}{f g n \log (F)}-\frac{18 a^2 b d^3 \left (F^{e g+f g x}\right )^n}{f^4 g^4 n^4 \log ^4(F)}+\frac{9 a b^2 d^2 (c+d x) \left (F^{e g+f g x}\right )^{2 n}}{4 f^3 g^3 n^3 \log ^3(F)}-\frac{9 a b^2 d (c+d x)^2 \left (F^{e g+f g x}\right )^{2 n}}{4 f^2 g^2 n^2 \log ^2(F)}+\frac{3 a b^2 (c+d x)^3 \left (F^{e g+f g x}\right )^{2 n}}{2 f g n \log (F)}-\frac{9 a b^2 d^3 \left (F^{e g+f g x}\right )^{2 n}}{8 f^4 g^4 n^4 \log ^4(F)}+\frac{2 b^3 d^2 (c+d x) \left (F^{e g+f g x}\right )^{3 n}}{9 f^3 g^3 n^3 \log ^3(F)}-\frac{b^3 d (c+d x)^2 \left (F^{e g+f g x}\right )^{3 n}}{3 f^2 g^2 n^2 \log ^2(F)}+\frac{b^3 (c+d x)^3 \left (F^{e g+f g x}\right )^{3 n}}{3 f g n \log (F)}-\frac{2 b^3 d^3 \left (F^{e g+f g x}\right )^{3 n}}{27 f^4 g^4 n^4 \log ^4(F)} \]

[Out]

(a^3*(c + d*x)^4)/(4*d) - (18*a^2*b*d^3*(F^(e*g + f*g*x))^n)/(f^4*g^4*n^4*Log[F]
^4) - (9*a*b^2*d^3*(F^(e*g + f*g*x))^(2*n))/(8*f^4*g^4*n^4*Log[F]^4) - (2*b^3*d^
3*(F^(e*g + f*g*x))^(3*n))/(27*f^4*g^4*n^4*Log[F]^4) + (18*a^2*b*d^2*(F^(e*g + f
*g*x))^n*(c + d*x))/(f^3*g^3*n^3*Log[F]^3) + (9*a*b^2*d^2*(F^(e*g + f*g*x))^(2*n
)*(c + d*x))/(4*f^3*g^3*n^3*Log[F]^3) + (2*b^3*d^2*(F^(e*g + f*g*x))^(3*n)*(c +
d*x))/(9*f^3*g^3*n^3*Log[F]^3) - (9*a^2*b*d*(F^(e*g + f*g*x))^n*(c + d*x)^2)/(f^
2*g^2*n^2*Log[F]^2) - (9*a*b^2*d*(F^(e*g + f*g*x))^(2*n)*(c + d*x)^2)/(4*f^2*g^2
*n^2*Log[F]^2) - (b^3*d*(F^(e*g + f*g*x))^(3*n)*(c + d*x)^2)/(3*f^2*g^2*n^2*Log[
F]^2) + (3*a^2*b*(F^(e*g + f*g*x))^n*(c + d*x)^3)/(f*g*n*Log[F]) + (3*a*b^2*(F^(
e*g + f*g*x))^(2*n)*(c + d*x)^3)/(2*f*g*n*Log[F]) + (b^3*(F^(e*g + f*g*x))^(3*n)
*(c + d*x)^3)/(3*f*g*n*Log[F])

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Rubi [A]  time = 1.23806, antiderivative size = 496, normalized size of antiderivative = 1., number of steps used = 14, number of rules used = 3, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.12 \[ \frac{a^3 (c+d x)^4}{4 d}+\frac{18 a^2 b d^2 (c+d x) \left (F^{e g+f g x}\right )^n}{f^3 g^3 n^3 \log ^3(F)}-\frac{9 a^2 b d (c+d x)^2 \left (F^{e g+f g x}\right )^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{3 a^2 b (c+d x)^3 \left (F^{e g+f g x}\right )^n}{f g n \log (F)}-\frac{18 a^2 b d^3 \left (F^{e g+f g x}\right )^n}{f^4 g^4 n^4 \log ^4(F)}+\frac{9 a b^2 d^2 (c+d x) \left (F^{e g+f g x}\right )^{2 n}}{4 f^3 g^3 n^3 \log ^3(F)}-\frac{9 a b^2 d (c+d x)^2 \left (F^{e g+f g x}\right )^{2 n}}{4 f^2 g^2 n^2 \log ^2(F)}+\frac{3 a b^2 (c+d x)^3 \left (F^{e g+f g x}\right )^{2 n}}{2 f g n \log (F)}-\frac{9 a b^2 d^3 \left (F^{e g+f g x}\right )^{2 n}}{8 f^4 g^4 n^4 \log ^4(F)}+\frac{2 b^3 d^2 (c+d x) \left (F^{e g+f g x}\right )^{3 n}}{9 f^3 g^3 n^3 \log ^3(F)}-\frac{b^3 d (c+d x)^2 \left (F^{e g+f g x}\right )^{3 n}}{3 f^2 g^2 n^2 \log ^2(F)}+\frac{b^3 (c+d x)^3 \left (F^{e g+f g x}\right )^{3 n}}{3 f g n \log (F)}-\frac{2 b^3 d^3 \left (F^{e g+f g x}\right )^{3 n}}{27 f^4 g^4 n^4 \log ^4(F)} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)^3,x]

[Out]

(a^3*(c + d*x)^4)/(4*d) - (18*a^2*b*d^3*(F^(e*g + f*g*x))^n)/(f^4*g^4*n^4*Log[F]
^4) - (9*a*b^2*d^3*(F^(e*g + f*g*x))^(2*n))/(8*f^4*g^4*n^4*Log[F]^4) - (2*b^3*d^
3*(F^(e*g + f*g*x))^(3*n))/(27*f^4*g^4*n^4*Log[F]^4) + (18*a^2*b*d^2*(F^(e*g + f
*g*x))^n*(c + d*x))/(f^3*g^3*n^3*Log[F]^3) + (9*a*b^2*d^2*(F^(e*g + f*g*x))^(2*n
)*(c + d*x))/(4*f^3*g^3*n^3*Log[F]^3) + (2*b^3*d^2*(F^(e*g + f*g*x))^(3*n)*(c +
d*x))/(9*f^3*g^3*n^3*Log[F]^3) - (9*a^2*b*d*(F^(e*g + f*g*x))^n*(c + d*x)^2)/(f^
2*g^2*n^2*Log[F]^2) - (9*a*b^2*d*(F^(e*g + f*g*x))^(2*n)*(c + d*x)^2)/(4*f^2*g^2
*n^2*Log[F]^2) - (b^3*d*(F^(e*g + f*g*x))^(3*n)*(c + d*x)^2)/(3*f^2*g^2*n^2*Log[
F]^2) + (3*a^2*b*(F^(e*g + f*g*x))^n*(c + d*x)^3)/(f*g*n*Log[F]) + (3*a*b^2*(F^(
e*g + f*g*x))^(2*n)*(c + d*x)^3)/(2*f*g*n*Log[F]) + (b^3*(F^(e*g + f*g*x))^(3*n)
*(c + d*x)^3)/(3*f*g*n*Log[F])

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Rubi in Sympy [A]  time = 174.116, size = 478, normalized size = 0.96 \[ \frac{a^{3} \left (c + d x\right )^{4}}{4 d} - \frac{18 a^{2} b d^{3} \left (F^{g \left (e + f x\right )}\right )^{n}}{f^{4} g^{4} n^{4} \log{\left (F \right )}^{4}} + \frac{18 a^{2} b d^{2} \left (c + d x\right ) \left (F^{g \left (e + f x\right )}\right )^{n}}{f^{3} g^{3} n^{3} \log{\left (F \right )}^{3}} - \frac{9 a^{2} b d \left (c + d x\right )^{2} \left (F^{g \left (e + f x\right )}\right )^{n}}{f^{2} g^{2} n^{2} \log{\left (F \right )}^{2}} + \frac{3 a^{2} b \left (c + d x\right )^{3} \left (F^{g \left (e + f x\right )}\right )^{n}}{f g n \log{\left (F \right )}} - \frac{9 a b^{2} d^{3} \left (F^{g \left (e + f x\right )}\right )^{2 n}}{8 f^{4} g^{4} n^{4} \log{\left (F \right )}^{4}} + \frac{9 a b^{2} d^{2} \left (c + d x\right ) \left (F^{g \left (e + f x\right )}\right )^{2 n}}{4 f^{3} g^{3} n^{3} \log{\left (F \right )}^{3}} - \frac{9 a b^{2} d \left (c + d x\right )^{2} \left (F^{g \left (e + f x\right )}\right )^{2 n}}{4 f^{2} g^{2} n^{2} \log{\left (F \right )}^{2}} + \frac{3 a b^{2} \left (c + d x\right )^{3} \left (F^{g \left (e + f x\right )}\right )^{2 n}}{2 f g n \log{\left (F \right )}} - \frac{2 b^{3} d^{3} \left (F^{g \left (e + f x\right )}\right )^{3 n}}{27 f^{4} g^{4} n^{4} \log{\left (F \right )}^{4}} + \frac{2 b^{3} d^{2} \left (c + d x\right ) \left (F^{g \left (e + f x\right )}\right )^{3 n}}{9 f^{3} g^{3} n^{3} \log{\left (F \right )}^{3}} - \frac{b^{3} d \left (c + d x\right )^{2} \left (F^{g \left (e + f x\right )}\right )^{3 n}}{3 f^{2} g^{2} n^{2} \log{\left (F \right )}^{2}} + \frac{b^{3} \left (c + d x\right )^{3} \left (F^{g \left (e + f x\right )}\right )^{3 n}}{3 f g n \log{\left (F \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b*(F**(g*(f*x+e)))**n)**3*(d*x+c)**3,x)

[Out]

a**3*(c + d*x)**4/(4*d) - 18*a**2*b*d**3*(F**(g*(e + f*x)))**n/(f**4*g**4*n**4*l
og(F)**4) + 18*a**2*b*d**2*(c + d*x)*(F**(g*(e + f*x)))**n/(f**3*g**3*n**3*log(F
)**3) - 9*a**2*b*d*(c + d*x)**2*(F**(g*(e + f*x)))**n/(f**2*g**2*n**2*log(F)**2)
+ 3*a**2*b*(c + d*x)**3*(F**(g*(e + f*x)))**n/(f*g*n*log(F)) - 9*a*b**2*d**3*(F
**(g*(e + f*x)))**(2*n)/(8*f**4*g**4*n**4*log(F)**4) + 9*a*b**2*d**2*(c + d*x)*(
F**(g*(e + f*x)))**(2*n)/(4*f**3*g**3*n**3*log(F)**3) - 9*a*b**2*d*(c + d*x)**2*
(F**(g*(e + f*x)))**(2*n)/(4*f**2*g**2*n**2*log(F)**2) + 3*a*b**2*(c + d*x)**3*(
F**(g*(e + f*x)))**(2*n)/(2*f*g*n*log(F)) - 2*b**3*d**3*(F**(g*(e + f*x)))**(3*n
)/(27*f**4*g**4*n**4*log(F)**4) + 2*b**3*d**2*(c + d*x)*(F**(g*(e + f*x)))**(3*n
)/(9*f**3*g**3*n**3*log(F)**3) - b**3*d*(c + d*x)**2*(F**(g*(e + f*x)))**(3*n)/(
3*f**2*g**2*n**2*log(F)**2) + b**3*(c + d*x)**3*(F**(g*(e + f*x)))**(3*n)/(3*f*g
*n*log(F))

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Mathematica [A]  time = 0.581917, size = 341, normalized size = 0.69 \[ a^3 c^3 x+\frac{3}{2} a^3 c^2 d x^2+a^3 c d^2 x^3+\frac{1}{4} a^3 d^3 x^4+\frac{3 a^2 b \left (F^{g (e+f x)}\right )^n \left (6 d^2 f g n \log (F) (c+d x)+f^3 g^3 n^3 \log ^3(F) (c+d x)^3-3 d f^2 g^2 n^2 \log ^2(F) (c+d x)^2-6 d^3\right )}{f^4 g^4 n^4 \log ^4(F)}+\frac{3 a b^2 \left (F^{g (e+f x)}\right )^{2 n} \left (6 d^2 f g n \log (F) (c+d x)+4 f^3 g^3 n^3 \log ^3(F) (c+d x)^3-6 d f^2 g^2 n^2 \log ^2(F) (c+d x)^2-3 d^3\right )}{8 f^4 g^4 n^4 \log ^4(F)}+\frac{b^3 \left (F^{g (e+f x)}\right )^{3 n} \left (6 d^2 f g n \log (F) (c+d x)+9 f^3 g^3 n^3 \log ^3(F) (c+d x)^3-9 d f^2 g^2 n^2 \log ^2(F) (c+d x)^2-2 d^3\right )}{27 f^4 g^4 n^4 \log ^4(F)} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)^3,x]

[Out]

a^3*c^3*x + (3*a^3*c^2*d*x^2)/2 + a^3*c*d^2*x^3 + (a^3*d^3*x^4)/4 + (3*a^2*b*(F^
(g*(e + f*x)))^n*(-6*d^3 + 6*d^2*f*g*n*(c + d*x)*Log[F] - 3*d*f^2*g^2*n^2*(c + d
*x)^2*Log[F]^2 + f^3*g^3*n^3*(c + d*x)^3*Log[F]^3))/(f^4*g^4*n^4*Log[F]^4) + (3*
a*b^2*(F^(g*(e + f*x)))^(2*n)*(-3*d^3 + 6*d^2*f*g*n*(c + d*x)*Log[F] - 6*d*f^2*g
^2*n^2*(c + d*x)^2*Log[F]^2 + 4*f^3*g^3*n^3*(c + d*x)^3*Log[F]^3))/(8*f^4*g^4*n^
4*Log[F]^4) + (b^3*(F^(g*(e + f*x)))^(3*n)*(-2*d^3 + 6*d^2*f*g*n*(c + d*x)*Log[F
] - 9*d*f^2*g^2*n^2*(c + d*x)^2*Log[F]^2 + 9*f^3*g^3*n^3*(c + d*x)^3*Log[F]^3))/
(27*f^4*g^4*n^4*Log[F]^4)

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Maple [F]  time = 0.032, size = 0, normalized size = 0. \[ \int \left ( a+b \left ({F}^{g \left ( fx+e \right ) } \right ) ^{n} \right ) ^{3} \left ( dx+c \right ) ^{3}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b*(F^(g*(f*x+e)))^n)^3*(d*x+c)^3,x)

[Out]

int((a+b*(F^(g*(f*x+e)))^n)^3*(d*x+c)^3,x)

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Maxima [F(-2)]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((F^((f*x + e)*g))^n*b + a)^3*(d*x + c)^3,x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [A]  time = 0.304978, size = 956, normalized size = 1.93 \[ \frac{54 \,{\left (a^{3} d^{3} f^{4} g^{4} n^{4} x^{4} + 4 \, a^{3} c d^{2} f^{4} g^{4} n^{4} x^{3} + 6 \, a^{3} c^{2} d f^{4} g^{4} n^{4} x^{2} + 4 \, a^{3} c^{3} f^{4} g^{4} n^{4} x\right )} \log \left (F\right )^{4} - 8 \,{\left (2 \, b^{3} d^{3} - 9 \,{\left (b^{3} d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, b^{3} c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, b^{3} c^{2} d f^{3} g^{3} n^{3} x + b^{3} c^{3} f^{3} g^{3} n^{3}\right )} \log \left (F\right )^{3} + 9 \,{\left (b^{3} d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{3} c d^{2} f^{2} g^{2} n^{2} x + b^{3} c^{2} d f^{2} g^{2} n^{2}\right )} \log \left (F\right )^{2} - 6 \,{\left (b^{3} d^{3} f g n x + b^{3} c d^{2} f g n\right )} \log \left (F\right )\right )} F^{3 \, f g n x + 3 \, e g n} - 81 \,{\left (3 \, a b^{2} d^{3} - 4 \,{\left (a b^{2} d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} g^{3} n^{3} x + a b^{2} c^{3} f^{3} g^{3} n^{3}\right )} \log \left (F\right )^{3} + 6 \,{\left (a b^{2} d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a b^{2} c d^{2} f^{2} g^{2} n^{2} x + a b^{2} c^{2} d f^{2} g^{2} n^{2}\right )} \log \left (F\right )^{2} - 6 \,{\left (a b^{2} d^{3} f g n x + a b^{2} c d^{2} f g n\right )} \log \left (F\right )\right )} F^{2 \, f g n x + 2 \, e g n} - 648 \,{\left (6 \, a^{2} b d^{3} -{\left (a^{2} b d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, a^{2} b c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, a^{2} b c^{2} d f^{3} g^{3} n^{3} x + a^{2} b c^{3} f^{3} g^{3} n^{3}\right )} \log \left (F\right )^{3} + 3 \,{\left (a^{2} b d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a^{2} b c d^{2} f^{2} g^{2} n^{2} x + a^{2} b c^{2} d f^{2} g^{2} n^{2}\right )} \log \left (F\right )^{2} - 6 \,{\left (a^{2} b d^{3} f g n x + a^{2} b c d^{2} f g n\right )} \log \left (F\right )\right )} F^{f g n x + e g n}}{216 \, f^{4} g^{4} n^{4} \log \left (F\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((F^((f*x + e)*g))^n*b + a)^3*(d*x + c)^3,x, algorithm="fricas")

[Out]

1/216*(54*(a^3*d^3*f^4*g^4*n^4*x^4 + 4*a^3*c*d^2*f^4*g^4*n^4*x^3 + 6*a^3*c^2*d*f
^4*g^4*n^4*x^2 + 4*a^3*c^3*f^4*g^4*n^4*x)*log(F)^4 - 8*(2*b^3*d^3 - 9*(b^3*d^3*f
^3*g^3*n^3*x^3 + 3*b^3*c*d^2*f^3*g^3*n^3*x^2 + 3*b^3*c^2*d*f^3*g^3*n^3*x + b^3*c
^3*f^3*g^3*n^3)*log(F)^3 + 9*(b^3*d^3*f^2*g^2*n^2*x^2 + 2*b^3*c*d^2*f^2*g^2*n^2*
x + b^3*c^2*d*f^2*g^2*n^2)*log(F)^2 - 6*(b^3*d^3*f*g*n*x + b^3*c*d^2*f*g*n)*log(
F))*F^(3*f*g*n*x + 3*e*g*n) - 81*(3*a*b^2*d^3 - 4*(a*b^2*d^3*f^3*g^3*n^3*x^3 + 3
*a*b^2*c*d^2*f^3*g^3*n^3*x^2 + 3*a*b^2*c^2*d*f^3*g^3*n^3*x + a*b^2*c^3*f^3*g^3*n
^3)*log(F)^3 + 6*(a*b^2*d^3*f^2*g^2*n^2*x^2 + 2*a*b^2*c*d^2*f^2*g^2*n^2*x + a*b^
2*c^2*d*f^2*g^2*n^2)*log(F)^2 - 6*(a*b^2*d^3*f*g*n*x + a*b^2*c*d^2*f*g*n)*log(F)
)*F^(2*f*g*n*x + 2*e*g*n) - 648*(6*a^2*b*d^3 - (a^2*b*d^3*f^3*g^3*n^3*x^3 + 3*a^
2*b*c*d^2*f^3*g^3*n^3*x^2 + 3*a^2*b*c^2*d*f^3*g^3*n^3*x + a^2*b*c^3*f^3*g^3*n^3)
*log(F)^3 + 3*(a^2*b*d^3*f^2*g^2*n^2*x^2 + 2*a^2*b*c*d^2*f^2*g^2*n^2*x + a^2*b*c
^2*d*f^2*g^2*n^2)*log(F)^2 - 6*(a^2*b*d^3*f*g*n*x + a^2*b*c*d^2*f*g*n)*log(F))*F
^(f*g*n*x + e*g*n))/(f^4*g^4*n^4*log(F)^4)

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Sympy [A]  time = 1.57344, size = 1074, normalized size = 2.17 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b*(F**(g*(f*x+e)))**n)**3*(d*x+c)**3,x)

[Out]

a**3*c**3*x + 3*a**3*c**2*d*x**2/2 + a**3*c*d**2*x**3 + a**3*d**3*x**4/4 + Piece
wise((((72*b**3*c**3*f**11*g**11*n**11*log(F)**11 + 216*b**3*c**2*d*f**11*g**11*
n**11*x*log(F)**11 - 72*b**3*c**2*d*f**10*g**10*n**10*log(F)**10 + 216*b**3*c*d*
*2*f**11*g**11*n**11*x**2*log(F)**11 - 144*b**3*c*d**2*f**10*g**10*n**10*x*log(F
)**10 + 48*b**3*c*d**2*f**9*g**9*n**9*log(F)**9 + 72*b**3*d**3*f**11*g**11*n**11
*x**3*log(F)**11 - 72*b**3*d**3*f**10*g**10*n**10*x**2*log(F)**10 + 48*b**3*d**3
*f**9*g**9*n**9*x*log(F)**9 - 16*b**3*d**3*f**8*g**8*n**8*log(F)**8)*(F**(g*(e +
f*x)))**(3*n) + (324*a*b**2*c**3*f**11*g**11*n**11*log(F)**11 + 972*a*b**2*c**2
*d*f**11*g**11*n**11*x*log(F)**11 - 486*a*b**2*c**2*d*f**10*g**10*n**10*log(F)**
10 + 972*a*b**2*c*d**2*f**11*g**11*n**11*x**2*log(F)**11 - 972*a*b**2*c*d**2*f**
10*g**10*n**10*x*log(F)**10 + 486*a*b**2*c*d**2*f**9*g**9*n**9*log(F)**9 + 324*a
*b**2*d**3*f**11*g**11*n**11*x**3*log(F)**11 - 486*a*b**2*d**3*f**10*g**10*n**10
*x**2*log(F)**10 + 486*a*b**2*d**3*f**9*g**9*n**9*x*log(F)**9 - 243*a*b**2*d**3*
f**8*g**8*n**8*log(F)**8)*(F**(g*(e + f*x)))**(2*n) + (648*a**2*b*c**3*f**11*g**
11*n**11*log(F)**11 + 1944*a**2*b*c**2*d*f**11*g**11*n**11*x*log(F)**11 - 1944*a
**2*b*c**2*d*f**10*g**10*n**10*log(F)**10 + 1944*a**2*b*c*d**2*f**11*g**11*n**11
*x**2*log(F)**11 - 3888*a**2*b*c*d**2*f**10*g**10*n**10*x*log(F)**10 + 3888*a**2
*b*c*d**2*f**9*g**9*n**9*log(F)**9 + 648*a**2*b*d**3*f**11*g**11*n**11*x**3*log(
F)**11 - 1944*a**2*b*d**3*f**10*g**10*n**10*x**2*log(F)**10 + 3888*a**2*b*d**3*f
**9*g**9*n**9*x*log(F)**9 - 3888*a**2*b*d**3*f**8*g**8*n**8*log(F)**8)*(F**(g*(e
+ f*x)))**n)/(216*f**12*g**12*n**12*log(F)**12), Ne(216*f**12*g**12*n**12*log(F
)**12, 0)), (x**4*(3*a**2*b*d**3/4 + 3*a*b**2*d**3/4 + b**3*d**3/4) + x**3*(3*a*
*2*b*c*d**2 + 3*a*b**2*c*d**2 + b**3*c*d**2) + x**2*(9*a**2*b*c**2*d/2 + 9*a*b**
2*c**2*d/2 + 3*b**3*c**2*d/2) + x*(3*a**2*b*c**3 + 3*a*b**2*c**3 + b**3*c**3), T
rue))

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.568073, size = 1, normalized size = 0. \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((F^((f*x + e)*g))^n*b + a)^3*(d*x + c)^3,x, algorithm="giac")

[Out]

Done