Optimal. Leaf size=594 \[ \frac {(c+d x)^4}{4 a^3 d}+\frac {3 d (c+d x)^2}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {3 d (c+d x)^2}{2 a^2 f^2 \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g^2 n^2 \log ^2(F)}-\frac {3 (c+d x)^3}{2 a^3 f g n \log (F)}+\frac {(c+d x)^3}{2 a f \left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 g n \log (F)}+\frac {(c+d x)^3}{a^2 f \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g n \log (F)}-\frac {3 d^2 (c+d x) \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac {9 d (c+d x)^2 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {(c+d x)^3 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f g n \log (F)}-\frac {3 d^3 \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^4 g^4 n^4 \log ^4(F)}+\frac {9 d^2 (c+d x) \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac {3 d (c+d x)^2 \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {9 d^3 \text {Li}_3\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^4 g^4 n^4 \log ^4(F)}+\frac {6 d^2 (c+d x) \text {Li}_3\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac {6 d^3 \text {Li}_4\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^4 g^4 n^4 \log ^4(F)} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 1.33, antiderivative size = 594, normalized size of antiderivative = 1.00, number of steps
used = 26, number of rules used = 10, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {2216, 2215,
2221, 2611, 6744, 2320, 6724, 2222, 2317, 2438} \begin {gather*} \frac {9 d^2 (c+d x) \text {PolyLog}\left (2,-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac {6 d^2 (c+d x) \text {PolyLog}\left (3,-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac {3 d (c+d x)^2 \text {PolyLog}\left (2,-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {3 d^3 \text {PolyLog}\left (2,-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^4 g^4 n^4 \log ^4(F)}-\frac {9 d^3 \text {PolyLog}\left (3,-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^4 g^4 n^4 \log ^4(F)}-\frac {6 d^3 \text {PolyLog}\left (4,-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^4 g^4 n^4 \log ^4(F)}-\frac {3 d^2 (c+d x) \log \left (\frac {b \left (F^{g (e+f x)}\right )^n}{a}+1\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac {9 d (c+d x)^2 \log \left (\frac {b \left (F^{g (e+f x)}\right )^n}{a}+1\right )}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {(c+d x)^3 \log \left (\frac {b \left (F^{g (e+f x)}\right )^n}{a}+1\right )}{a^3 f g n \log (F)}+\frac {3 d (c+d x)^2}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {3 (c+d x)^3}{2 a^3 f g n \log (F)}+\frac {(c+d x)^4}{4 a^3 d}-\frac {3 d (c+d x)^2}{2 a^2 f^2 g^2 n^2 \log ^2(F) \left (a+b \left (F^{g (e+f x)}\right )^n\right )}+\frac {(c+d x)^3}{a^2 f g n \log (F) \left (a+b \left (F^{g (e+f x)}\right )^n\right )}+\frac {(c+d x)^3}{2 a f g n \log (F) \left (a+b \left (F^{g (e+f x)}\right )^n\right )^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2215
Rule 2216
Rule 2221
Rule 2222
Rule 2317
Rule 2320
Rule 2438
Rule 2611
Rule 6724
Rule 6744
Rubi steps
\begin {align*} \int \frac {(c+d x)^3}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^3} \, dx &=\frac {\int \frac {(c+d x)^3}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2} \, dx}{a}-\frac {b \int \frac {\left (F^{g (e+f x)}\right )^n (c+d x)^3}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^3} \, dx}{a}\\ &=\frac {(c+d x)^3}{2 a f \left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 g n \log (F)}+\frac {\int \frac {(c+d x)^3}{a+b \left (F^{g (e+f x)}\right )^n} \, dx}{a^2}-\frac {b \int \frac {\left (F^{g (e+f x)}\right )^n (c+d x)^3}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2} \, dx}{a^2}-\frac {(3 d) \int \frac {(c+d x)^2}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2} \, dx}{2 a f g n \log (F)}\\ &=\frac {(c+d x)^4}{4 a^3 d}+\frac {(c+d x)^3}{2 a f \left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 g n \log (F)}+\frac {(c+d x)^3}{a^2 f \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g n \log (F)}-\frac {b \int \frac {\left (F^{g (e+f x)}\right )^n (c+d x)^3}{a+b \left (F^{g (e+f x)}\right )^n} \, dx}{a^3}-\frac {(3 d) \int \frac {(c+d x)^2}{a+b \left (F^{g (e+f x)}\right )^n} \, dx}{2 a^2 f g n \log (F)}-\frac {(3 d) \int \frac {(c+d x)^2}{a+b \left (F^{g (e+f x)}\right )^n} \, dx}{a^2 f g n \log (F)}+\frac {(3 b d) \int \frac {\left (F^{g (e+f x)}\right )^n (c+d x)^2}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2} \, dx}{2 a^2 f g n \log (F)}\\ &=\frac {(c+d x)^4}{4 a^3 d}-\frac {3 d (c+d x)^2}{2 a^2 f^2 \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g^2 n^2 \log ^2(F)}-\frac {3 (c+d x)^3}{2 a^3 f g n \log (F)}+\frac {(c+d x)^3}{2 a f \left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 g n \log (F)}+\frac {(c+d x)^3}{a^2 f \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g n \log (F)}-\frac {(c+d x)^3 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f g n \log (F)}+\frac {\left (3 d^2\right ) \int \frac {c+d x}{a+b \left (F^{g (e+f x)}\right )^n} \, dx}{a^2 f^2 g^2 n^2 \log ^2(F)}+\frac {(3 d) \int (c+d x)^2 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right ) \, dx}{a^3 f g n \log (F)}+\frac {(3 b d) \int \frac {\left (F^{g (e+f x)}\right )^n (c+d x)^2}{a+b \left (F^{g (e+f x)}\right )^n} \, dx}{2 a^3 f g n \log (F)}+\frac {(3 b d) \int \frac {\left (F^{g (e+f x)}\right )^n (c+d x)^2}{a+b \left (F^{g (e+f x)}\right )^n} \, dx}{a^3 f g n \log (F)}\\ &=\frac {(c+d x)^4}{4 a^3 d}+\frac {3 d (c+d x)^2}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {3 d (c+d x)^2}{2 a^2 f^2 \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g^2 n^2 \log ^2(F)}-\frac {3 (c+d x)^3}{2 a^3 f g n \log (F)}+\frac {(c+d x)^3}{2 a f \left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 g n \log (F)}+\frac {(c+d x)^3}{a^2 f \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g n \log (F)}+\frac {9 d (c+d x)^2 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {(c+d x)^3 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f g n \log (F)}-\frac {3 d (c+d x)^2 \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {\left (3 d^2\right ) \int (c+d x) \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right ) \, dx}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {\left (6 d^2\right ) \int (c+d x) \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right ) \, dx}{a^3 f^2 g^2 n^2 \log ^2(F)}+\frac {\left (6 d^2\right ) \int (c+d x) \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right ) \, dx}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {\left (3 b d^2\right ) \int \frac {\left (F^{g (e+f x)}\right )^n (c+d x)}{a+b \left (F^{g (e+f x)}\right )^n} \, dx}{a^3 f^2 g^2 n^2 \log ^2(F)}\\ &=\frac {(c+d x)^4}{4 a^3 d}+\frac {3 d (c+d x)^2}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {3 d (c+d x)^2}{2 a^2 f^2 \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g^2 n^2 \log ^2(F)}-\frac {3 (c+d x)^3}{2 a^3 f g n \log (F)}+\frac {(c+d x)^3}{2 a f \left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 g n \log (F)}+\frac {(c+d x)^3}{a^2 f \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g n \log (F)}-\frac {3 d^2 (c+d x) \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac {9 d (c+d x)^2 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {(c+d x)^3 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f g n \log (F)}+\frac {9 d^2 (c+d x) \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac {3 d (c+d x)^2 \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^2 g^2 n^2 \log ^2(F)}+\frac {6 d^2 (c+d x) \text {Li}_3\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac {\left (3 d^3\right ) \int \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right ) \, dx}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac {\left (3 d^3\right ) \int \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right ) \, dx}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac {\left (6 d^3\right ) \int \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right ) \, dx}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac {\left (6 d^3\right ) \int \text {Li}_3\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right ) \, dx}{a^3 f^3 g^3 n^3 \log ^3(F)}\\ &=\frac {(c+d x)^4}{4 a^3 d}+\frac {3 d (c+d x)^2}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {3 d (c+d x)^2}{2 a^2 f^2 \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g^2 n^2 \log ^2(F)}-\frac {3 (c+d x)^3}{2 a^3 f g n \log (F)}+\frac {(c+d x)^3}{2 a f \left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 g n \log (F)}+\frac {(c+d x)^3}{a^2 f \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g n \log (F)}-\frac {3 d^2 (c+d x) \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac {9 d (c+d x)^2 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {(c+d x)^3 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f g n \log (F)}+\frac {9 d^2 (c+d x) \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac {3 d (c+d x)^2 \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^2 g^2 n^2 \log ^2(F)}+\frac {6 d^2 (c+d x) \text {Li}_3\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac {\left (3 d^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{a}\right )}{x} \, dx,x,\left (F^{g (e+f x)}\right )^n\right )}{a^3 f^4 g^4 n^4 \log ^4(F)}-\frac {\left (3 d^3\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b x^n}{a}\right )}{x} \, dx,x,F^{g (e+f x)}\right )}{a^3 f^4 g^4 n^3 \log ^4(F)}-\frac {\left (6 d^3\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b x^n}{a}\right )}{x} \, dx,x,F^{g (e+f x)}\right )}{a^3 f^4 g^4 n^3 \log ^4(F)}-\frac {\left (6 d^3\right ) \text {Subst}\left (\int \frac {\text {Li}_3\left (-\frac {b x^n}{a}\right )}{x} \, dx,x,F^{g (e+f x)}\right )}{a^3 f^4 g^4 n^3 \log ^4(F)}\\ &=\frac {(c+d x)^4}{4 a^3 d}+\frac {3 d (c+d x)^2}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {3 d (c+d x)^2}{2 a^2 f^2 \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g^2 n^2 \log ^2(F)}-\frac {3 (c+d x)^3}{2 a^3 f g n \log (F)}+\frac {(c+d x)^3}{2 a f \left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 g n \log (F)}+\frac {(c+d x)^3}{a^2 f \left (a+b \left (F^{g (e+f x)}\right )^n\right ) g n \log (F)}-\frac {3 d^2 (c+d x) \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac {9 d (c+d x)^2 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {(c+d x)^3 \log \left (1+\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f g n \log (F)}-\frac {3 d^3 \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^4 g^4 n^4 \log ^4(F)}+\frac {9 d^2 (c+d x) \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac {3 d (c+d x)^2 \text {Li}_2\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac {9 d^3 \text {Li}_3\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^4 g^4 n^4 \log ^4(F)}+\frac {6 d^2 (c+d x) \text {Li}_3\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac {6 d^3 \text {Li}_4\left (-\frac {b \left (F^{g (e+f x)}\right )^n}{a}\right )}{a^3 f^4 g^4 n^4 \log ^4(F)}\\ \end {align*}
________________________________________________________________________________________
Mathematica [F]
time = 1.79, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(c+d x)^3}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^3} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(4004\) vs.
\(2(582)=1164\).
time = 0.09, size = 4005, normalized size = 6.74
method | result | size |
risch | \(\text {Expression too large to display}\) | \(4005\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.42, size = 1028, normalized size = 1.73 \begin {gather*} \frac {1}{2} \, c^{3} {\left (\frac {2 \, F^{f g n x + g n e} b + 3 \, a}{{\left (2 \, F^{f g n x + g n e} a^{3} b + F^{2 \, f g n x + 2 \, g n e} a^{2} b^{2} + a^{4}\right )} f g n \log \left (F\right )} + \frac {2 \, {\left (f g n x + g n e\right )}}{a^{3} f g n} - \frac {2 \, \log \left (F^{f g n x + g n e} b + a\right )}{a^{3} f g n \log \left (F\right )}\right )} + \frac {3 \, a d^{3} f g n x^{3} \log \left (F\right ) - 3 \, a c^{2} d + 3 \, {\left (3 \, a c d^{2} f g n \log \left (F\right ) - a d^{3}\right )} x^{2} + {\left (2 \, F^{g n e} b d^{3} f g n x^{3} \log \left (F\right ) - 3 \, F^{g n e} b c^{2} d + 3 \, {\left (2 \, F^{g n e} b c d^{2} f g n \log \left (F\right ) - F^{g n e} b d^{3}\right )} x^{2} + 6 \, {\left (F^{g n e} b c^{2} d f g n \log \left (F\right ) - F^{g n e} b c d^{2}\right )} x\right )} F^{f g n x} + 3 \, {\left (3 \, a c^{2} d f g n \log \left (F\right ) - 2 \, a c d^{2}\right )} x}{2 \, {\left (2 \, F^{f g n x} F^{g n e} a^{3} b f^{2} g^{2} n^{2} \log \left (F\right )^{2} + F^{2 \, f g n x} F^{2 \, g n e} a^{2} b^{2} f^{2} g^{2} n^{2} \log \left (F\right )^{2} + a^{4} f^{2} g^{2} n^{2} \log \left (F\right )^{2}\right )}} - \frac {3 \, {\left (3 \, c^{2} d f g n \log \left (F\right ) - 2 \, c d^{2}\right )} x}{2 \, a^{3} f^{2} g^{2} n^{2} \log \left (F\right )^{2}} + \frac {3 \, {\left (3 \, c^{2} d f g n \log \left (F\right ) - 2 \, c d^{2}\right )} \log \left (F^{f g n x} F^{g n e} b + a\right )}{2 \, a^{3} f^{3} g^{3} n^{3} \log \left (F\right )^{3}} - \frac {{\left (f^{3} g^{3} n^{3} x^{3} \log \left (\frac {F^{f g n x} F^{g n e} b}{a} + 1\right ) \log \left (F\right )^{3} + 3 \, f^{2} g^{2} n^{2} x^{2} {\rm Li}_2\left (-\frac {F^{f g n x} F^{g n e} b}{a}\right ) \log \left (F\right )^{2} - 6 \, f g n x \log \left (F\right ) {\rm Li}_{3}(-\frac {F^{f g n x} F^{g n e} b}{a}) + 6 \, {\rm Li}_{4}(-\frac {F^{f g n x} F^{g n e} b}{a})\right )} d^{3}}{a^{3} f^{4} g^{4} n^{4} \log \left (F\right )^{4}} - \frac {3 \, {\left (f^{2} g^{2} n^{2} x^{2} \log \left (\frac {F^{f g n x} F^{g n e} b}{a} + 1\right ) \log \left (F\right )^{2} + 2 \, f g n x {\rm Li}_2\left (-\frac {F^{f g n x} F^{g n e} b}{a}\right ) \log \left (F\right ) - 2 \, {\rm Li}_{3}(-\frac {F^{f g n x} F^{g n e} b}{a})\right )} {\left (2 \, c d^{2} f g n \log \left (F\right ) - 3 \, d^{3}\right )}}{2 \, a^{3} f^{4} g^{4} n^{4} \log \left (F\right )^{4}} - \frac {3 \, {\left (c^{2} d f^{2} g^{2} n^{2} \log \left (F\right )^{2} - 3 \, c d^{2} f g n \log \left (F\right ) + d^{3}\right )} {\left (f g n x \log \left (\frac {F^{f g n x} F^{g n e} b}{a} + 1\right ) \log \left (F\right ) + {\rm Li}_2\left (-\frac {F^{f g n x} F^{g n e} b}{a}\right )\right )}}{a^{3} f^{4} g^{4} n^{4} \log \left (F\right )^{4}} + \frac {d^{3} f^{4} g^{4} n^{4} x^{4} \log \left (F\right )^{4} + 2 \, {\left (2 \, c d^{2} f g n \log \left (F\right ) - 3 \, d^{3}\right )} f^{3} g^{3} n^{3} x^{3} \log \left (F\right )^{3} + 6 \, {\left (c^{2} d f^{2} g^{2} n^{2} \log \left (F\right )^{2} - 3 \, c d^{2} f g n \log \left (F\right ) + d^{3}\right )} f^{2} g^{2} n^{2} x^{2} \log \left (F\right )^{2}}{4 \, a^{3} f^{4} g^{4} n^{4} \log \left (F\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 2968 vs.
\(2 (591) = 1182\).
time = 0.46, size = 2968, normalized size = 5.00 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {3 a c^{3} f g n \log {\left (F \right )} + 9 a c^{2} d f g n x \log {\left (F \right )} - 3 a c^{2} d + 9 a c d^{2} f g n x^{2} \log {\left (F \right )} - 6 a c d^{2} x + 3 a d^{3} f g n x^{3} \log {\left (F \right )} - 3 a d^{3} x^{2} + \left (2 b c^{3} f g n \log {\left (F \right )} + 6 b c^{2} d f g n x \log {\left (F \right )} - 3 b c^{2} d + 6 b c d^{2} f g n x^{2} \log {\left (F \right )} - 6 b c d^{2} x + 2 b d^{3} f g n x^{3} \log {\left (F \right )} - 3 b d^{3} x^{2}\right ) \left (F^{g \left (e + f x\right )}\right )^{n}}{2 a^{4} f^{2} g^{2} n^{2} \log {\left (F \right )}^{2} + 4 a^{3} b f^{2} g^{2} n^{2} \left (F^{g \left (e + f x\right )}\right )^{n} \log {\left (F \right )}^{2} + 2 a^{2} b^{2} f^{2} g^{2} n^{2} \left (F^{g \left (e + f x\right )}\right )^{2 n} \log {\left (F \right )}^{2}} + \frac {\int \frac {6 c d^{2}}{a + b e^{e g n \log {\left (F \right )}} e^{f g n x \log {\left (F \right )}}}\, dx + \int \frac {6 d^{3} x}{a + b e^{e g n \log {\left (F \right )}} e^{f g n x \log {\left (F \right )}}}\, dx + \int \frac {2 c^{3} f^{2} g^{2} n^{2} \log {\left (F \right )}^{2}}{a + b e^{e g n \log {\left (F \right )}} e^{f g n x \log {\left (F \right )}}}\, dx + \int \left (- \frac {9 c^{2} d f g n \log {\left (F \right )}}{a + b e^{e g n \log {\left (F \right )}} e^{f g n x \log {\left (F \right )}}}\right )\, dx + \int \left (- \frac {9 d^{3} f g n x^{2} \log {\left (F \right )}}{a + b e^{e g n \log {\left (F \right )}} e^{f g n x \log {\left (F \right )}}}\right )\, dx + \int \frac {2 d^{3} f^{2} g^{2} n^{2} x^{3} \log {\left (F \right )}^{2}}{a + b e^{e g n \log {\left (F \right )}} e^{f g n x \log {\left (F \right )}}}\, dx + \int \left (- \frac {18 c d^{2} f g n x \log {\left (F \right )}}{a + b e^{e g n \log {\left (F \right )}} e^{f g n x \log {\left (F \right )}}}\right )\, dx + \int \frac {6 c d^{2} f^{2} g^{2} n^{2} x^{2} \log {\left (F \right )}^{2}}{a + b e^{e g n \log {\left (F \right )}} e^{f g n x \log {\left (F \right )}}}\, dx + \int \frac {6 c^{2} d f^{2} g^{2} n^{2} x \log {\left (F \right )}^{2}}{a + b e^{e g n \log {\left (F \right )}} e^{f g n x \log {\left (F \right )}}}\, dx}{2 a^{2} f^{2} g^{2} n^{2} \log {\left (F \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {{\left (c+d\,x\right )}^3}{{\left (a+b\,{\left (F^{g\,\left (e+f\,x\right )}\right )}^n\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________