Optimal. Leaf size=451 \[ \frac {3 b^2 e^3 n^2 \text {Li}_2\left (\frac {d}{d+\frac {e}{x^{2/3}}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{d^3}+\frac {3 b^2 e^3 n^2 \log \left (1-\frac {d}{d+\frac {e}{x^{2/3}}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{2 d^3}+\frac {3 b^2 e^3 n^2 \log \left (-\frac {e}{d x^{2/3}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{d^3}+\frac {3 b^2 e^2 n^2 x^{2/3} \left (d+\frac {e}{x^{2/3}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{2 d^3}-\frac {3 b e^3 n \log \left (1-\frac {d}{d+\frac {e}{x^{2/3}}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{2 d^3}-\frac {3 b e^2 n x^{2/3} \left (d+\frac {e}{x^{2/3}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{2 d^3}+\frac {3 b e n x^{4/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{4 d}+\frac {1}{2} x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3-\frac {3 b^3 e^3 n^3 \text {Li}_2\left (\frac {d}{d+\frac {e}{x^{2/3}}}\right )}{2 d^3}+\frac {3 b^3 e^3 n^3 \text {Li}_2\left (\frac {e}{d x^{2/3}}+1\right )}{d^3}+\frac {3 b^3 e^3 n^3 \text {Li}_3\left (\frac {d}{d+\frac {e}{x^{2/3}}}\right )}{d^3}+\frac {b^3 e^3 n^3 \log (x)}{d^3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 1.00, antiderivative size = 428, normalized size of antiderivative = 0.95, number of steps used = 22, number of rules used = 16, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.727, Rules used = {2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31} \[ -\frac {3 b^2 e^3 n^2 \text {PolyLog}\left (2,\frac {e}{d x^{2/3}}+1\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{d^3}+\frac {9 b^3 e^3 n^3 \text {PolyLog}\left (2,\frac {e}{d x^{2/3}}+1\right )}{2 d^3}+\frac {3 b^3 e^3 n^3 \text {PolyLog}\left (3,\frac {e}{d x^{2/3}}+1\right )}{d^3}+\frac {9 b^2 e^3 n^2 \log \left (-\frac {e}{d x^{2/3}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{2 d^3}+\frac {3 b^2 e^2 n^2 x^{2/3} \left (d+\frac {e}{x^{2/3}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{2 d^3}+\frac {e^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3}{2 d^3}-\frac {3 b e^3 n \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{4 d^3}-\frac {3 b e^3 n \log \left (-\frac {e}{d x^{2/3}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{2 d^3}-\frac {3 b e^2 n x^{2/3} \left (d+\frac {e}{x^{2/3}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{2 d^3}+\frac {3 b e n x^{4/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{4 d}+\frac {1}{2} x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {b^3 e^3 n^3 \log (x)}{d^3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 30
Rule 31
Rule 2301
Rule 2302
Rule 2314
Rule 2317
Rule 2318
Rule 2319
Rule 2344
Rule 2347
Rule 2374
Rule 2391
Rule 2398
Rule 2411
Rule 2454
Rule 6589
Rubi steps
\begin {align*} \int x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3 \, dx &=-\left (\frac {3}{2} \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^3}{x^4} \, dx,x,\frac {1}{x^{2/3}}\right )\right )\\ &=\frac {1}{2} x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3-\frac {1}{2} (3 b e n) \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^2}{x^3 (d+e x)} \, dx,x,\frac {1}{x^{2/3}}\right )\\ &=\frac {1}{2} x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3-\frac {1}{2} (3 b n) \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^3} \, dx,x,d+\frac {e}{x^{2/3}}\right )\\ &=\frac {1}{2} x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3-\frac {(3 b n) \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{\left (-\frac {d}{e}+\frac {x}{e}\right )^3} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d}+\frac {(3 b e n) \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^2} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d}\\ &=\frac {3 b e n x^{4/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{4 d}+\frac {1}{2} x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {(3 b e n) \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{\left (-\frac {d}{e}+\frac {x}{e}\right )^2} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d^2}-\frac {\left (3 b e^2 n\right ) \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{x \left (-\frac {d}{e}+\frac {x}{e}\right )} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d^2}-\frac {\left (3 b^2 e n^2\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^2} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d}\\ &=-\frac {3 b e^2 n \left (d+\frac {e}{x^{2/3}}\right ) x^{2/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{2 d^3}+\frac {3 b e n x^{4/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{4 d}+\frac {1}{2} x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3-\frac {\left (3 b e^2 n\right ) \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{-\frac {d}{e}+\frac {x}{e}} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d^3}+\frac {\left (3 b e^3 n\right ) \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{x} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d^3}-\frac {\left (3 b^2 e n^2\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{\left (-\frac {d}{e}+\frac {x}{e}\right )^2} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d^2}+\frac {\left (3 b^2 e^2 n^2\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{-\frac {d}{e}+\frac {x}{e}} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{d^3}+\frac {\left (3 b^2 e^2 n^2\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{x \left (-\frac {d}{e}+\frac {x}{e}\right )} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d^2}\\ &=\frac {3 b^2 e^2 n^2 \left (d+\frac {e}{x^{2/3}}\right ) x^{2/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{2 d^3}-\frac {3 b e^2 n \left (d+\frac {e}{x^{2/3}}\right ) x^{2/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{2 d^3}+\frac {3 b e n x^{4/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{4 d}+\frac {1}{2} x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {3 b^2 e^3 n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (-\frac {e}{d x^{2/3}}\right )}{d^3}-\frac {3 b e^3 n \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2 \log \left (-\frac {e}{d x^{2/3}}\right )}{2 d^3}+\frac {\left (3 e^3\right ) \operatorname {Subst}\left (\int x^2 \, dx,x,a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{2 d^3}+\frac {\left (3 b^2 e^2 n^2\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{-\frac {d}{e}+\frac {x}{e}} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d^3}-\frac {\left (3 b^2 e^3 n^2\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{x} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d^3}+\frac {\left (3 b^2 e^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right ) \log \left (1-\frac {x}{d}\right )}{x} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{d^3}-\frac {\left (3 b^3 e^2 n^3\right ) \operatorname {Subst}\left (\int \frac {1}{-\frac {d}{e}+\frac {x}{e}} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d^3}-\frac {\left (3 b^3 e^3 n^3\right ) \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {x}{d}\right )}{x} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{d^3}\\ &=\frac {3 b^2 e^2 n^2 \left (d+\frac {e}{x^{2/3}}\right ) x^{2/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{2 d^3}-\frac {3 b e^3 n \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{4 d^3}-\frac {3 b e^2 n \left (d+\frac {e}{x^{2/3}}\right ) x^{2/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{2 d^3}+\frac {3 b e n x^{4/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{4 d}+\frac {e^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3}{2 d^3}+\frac {1}{2} x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {9 b^2 e^3 n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (-\frac {e}{d x^{2/3}}\right )}{2 d^3}-\frac {3 b e^3 n \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2 \log \left (-\frac {e}{d x^{2/3}}\right )}{2 d^3}+\frac {b^3 e^3 n^3 \log (x)}{d^3}+\frac {3 b^3 e^3 n^3 \text {Li}_2\left (1+\frac {e}{d x^{2/3}}\right )}{d^3}-\frac {3 b^2 e^3 n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \text {Li}_2\left (1+\frac {e}{d x^{2/3}}\right )}{d^3}-\frac {\left (3 b^3 e^3 n^3\right ) \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {x}{d}\right )}{x} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{2 d^3}+\frac {\left (3 b^3 e^3 n^3\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (\frac {x}{d}\right )}{x} \, dx,x,d+\frac {e}{x^{2/3}}\right )}{d^3}\\ &=\frac {3 b^2 e^2 n^2 \left (d+\frac {e}{x^{2/3}}\right ) x^{2/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{2 d^3}-\frac {3 b e^3 n \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{4 d^3}-\frac {3 b e^2 n \left (d+\frac {e}{x^{2/3}}\right ) x^{2/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{2 d^3}+\frac {3 b e n x^{4/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{4 d}+\frac {e^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3}{2 d^3}+\frac {1}{2} x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {9 b^2 e^3 n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (-\frac {e}{d x^{2/3}}\right )}{2 d^3}-\frac {3 b e^3 n \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2 \log \left (-\frac {e}{d x^{2/3}}\right )}{2 d^3}+\frac {b^3 e^3 n^3 \log (x)}{d^3}+\frac {9 b^3 e^3 n^3 \text {Li}_2\left (1+\frac {e}{d x^{2/3}}\right )}{2 d^3}-\frac {3 b^2 e^3 n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \text {Li}_2\left (1+\frac {e}{d x^{2/3}}\right )}{d^3}+\frac {3 b^3 e^3 n^3 \text {Li}_3\left (1+\frac {e}{d x^{2/3}}\right )}{d^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 1.42, size = 683, normalized size = 1.51 \[ \frac {6 b^2 n^2 \left (\left (d^3 x^2+e^3\right ) \log ^2\left (d+\frac {e}{x^{2/3}}\right )+e \log \left (d+\frac {e}{x^{2/3}}\right ) \left (d^2 x^{4/3}-2 e^2 \log \left (-\frac {e}{d x^{2/3}}\right )-2 d e x^{2/3}-3 e^2\right )-2 e^3 \text {Li}_2\left (\frac {e}{d x^{2/3}}+1\right )+e^2 \left (3 e \log \left (-\frac {e}{d x^{2/3}}\right )+d x^{2/3}\right )\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )-b n \log \left (d+\frac {e}{x^{2/3}}\right )\right )+2 d^3 x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )-b n \log \left (d+\frac {e}{x^{2/3}}\right )\right )^3+6 b d^3 n x^2 \log \left (d+\frac {e}{x^{2/3}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )-b n \log \left (d+\frac {e}{x^{2/3}}\right )\right )^2+3 b d^2 e n x^{4/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )-b n \log \left (d+\frac {e}{x^{2/3}}\right )\right )^2+6 b e^3 n \log \left (d x^{2/3}+e\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )-b n \log \left (d+\frac {e}{x^{2/3}}\right )\right )^2-6 b d e^2 n x^{2/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )-b n \log \left (d+\frac {e}{x^{2/3}}\right )\right )^2-b^3 n^3 \left (-2 d^3 x^2 \log ^3\left (d+\frac {e}{x^{2/3}}\right )-3 d^2 e x^{4/3} \log ^2\left (d+\frac {e}{x^{2/3}}\right )-12 e^3 \text {Li}_3\left (\frac {e}{d x^{2/3}}+1\right )+6 e^3 \text {Li}_2\left (\frac {e}{d x^{2/3}}+1\right ) \left (2 \log \left (d+\frac {e}{x^{2/3}}\right )-3\right )-2 e^3 \log ^3\left (d+\frac {e}{x^{2/3}}\right )+9 e^3 \log ^2\left (d+\frac {e}{x^{2/3}}\right )+6 e^3 \log ^2\left (d+\frac {e}{x^{2/3}}\right ) \log \left (-\frac {e}{d x^{2/3}}\right )-6 e^3 \log \left (d+\frac {e}{x^{2/3}}\right )-18 e^3 \log \left (d+\frac {e}{x^{2/3}}\right ) \log \left (-\frac {e}{d x^{2/3}}\right )+6 e^3 \log \left (-\frac {e}{d x^{2/3}}\right )+6 d e^2 x^{2/3} \log ^2\left (d+\frac {e}{x^{2/3}}\right )-6 d e^2 x^{2/3} \log \left (d+\frac {e}{x^{2/3}}\right )\right )}{4 d^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [F] time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (b^{3} x \log \left (c \left (\frac {d x + e x^{\frac {1}{3}}}{x}\right )^{n}\right )^{3} + 3 \, a b^{2} x \log \left (c \left (\frac {d x + e x^{\frac {1}{3}}}{x}\right )^{n}\right )^{2} + 3 \, a^{2} b x \log \left (c \left (\frac {d x + e x^{\frac {1}{3}}}{x}\right )^{n}\right ) + a^{3} x, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \log \left (c {\left (d + \frac {e}{x^{\frac {2}{3}}}\right )}^{n}\right ) + a\right )}^{3} x\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [F] time = 0.19, size = 0, normalized size = 0.00 \[ \int \left (b \ln \left (c \left (d +\frac {e}{x^{\frac {2}{3}}}\right )^{n}\right )+a \right )^{3} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {1}{2} \, b^{3} n^{3} x^{2} \log \left (d x^{\frac {2}{3}} + e\right )^{3} - \int \frac {{\left (b^{3} d n x^{2} - 3 \, {\left (b^{3} d \log \relax (c) + a b^{2} d\right )} x^{2} - 3 \, {\left (b^{3} e \log \relax (c) + a b^{2} e\right )} x^{\frac {4}{3}} + 6 \, {\left (b^{3} d x^{2} + b^{3} e x^{\frac {4}{3}}\right )} \log \left (x^{\frac {1}{3} \, n}\right )\right )} n^{2} \log \left (d x^{\frac {2}{3}} + e\right )^{2} + 8 \, {\left (b^{3} d x^{2} + b^{3} e x^{\frac {4}{3}}\right )} \log \left (x^{\frac {1}{3} \, n}\right )^{3} - {\left (b^{3} d \log \relax (c)^{3} + 3 \, a b^{2} d \log \relax (c)^{2} + 3 \, a^{2} b d \log \relax (c) + a^{3} d\right )} x^{2} - 3 \, {\left ({\left (b^{3} d \log \relax (c)^{2} + 2 \, a b^{2} d \log \relax (c) + a^{2} b d\right )} x^{2} + 4 \, {\left (b^{3} d x^{2} + b^{3} e x^{\frac {4}{3}}\right )} \log \left (x^{\frac {1}{3} \, n}\right )^{2} + {\left (b^{3} e \log \relax (c)^{2} + 2 \, a b^{2} e \log \relax (c) + a^{2} b e\right )} x^{\frac {4}{3}} - 4 \, {\left ({\left (b^{3} d \log \relax (c) + a b^{2} d\right )} x^{2} + {\left (b^{3} e \log \relax (c) + a b^{2} e\right )} x^{\frac {4}{3}}\right )} \log \left (x^{\frac {1}{3} \, n}\right )\right )} n \log \left (d x^{\frac {2}{3}} + e\right ) - 12 \, {\left ({\left (b^{3} d \log \relax (c) + a b^{2} d\right )} x^{2} + {\left (b^{3} e \log \relax (c) + a b^{2} e\right )} x^{\frac {4}{3}}\right )} \log \left (x^{\frac {1}{3} \, n}\right )^{2} - {\left (b^{3} e \log \relax (c)^{3} + 3 \, a b^{2} e \log \relax (c)^{2} + 3 \, a^{2} b e \log \relax (c) + a^{3} e\right )} x^{\frac {4}{3}} + 6 \, {\left ({\left (b^{3} d \log \relax (c)^{2} + 2 \, a b^{2} d \log \relax (c) + a^{2} b d\right )} x^{2} + {\left (b^{3} e \log \relax (c)^{2} + 2 \, a b^{2} e \log \relax (c) + a^{2} b e\right )} x^{\frac {4}{3}}\right )} \log \left (x^{\frac {1}{3} \, n}\right )}{d x + e x^{\frac {1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int x\,{\left (a+b\,\ln \left (c\,{\left (d+\frac {e}{x^{2/3}}\right )}^n\right )\right )}^3 \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________