Optimal. Leaf size=603 \[ \frac {3}{4} b^2 n^2 x^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (d (e+f x)^m\right )+\frac {3 b^2 e^2 m n^2 \text {Li}_2\left (-\frac {f x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )}{2 f^2}+\frac {3 b^2 e^2 m n^2 \text {Li}_3\left (-\frac {f x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )}{f^2}-\frac {3 b^2 e^2 m n^2 \log \left (\frac {f x}{e}+1\right ) \left (a+b \log \left (c x^n\right )\right )}{4 f^2}-\frac {9}{8} b^2 m n^2 x^2 \left (a+b \log \left (c x^n\right )\right )+\frac {21 a b^2 e m n^2 x}{4 f}-\frac {3}{4} b n x^2 \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+\frac {1}{2} x^2 \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-\frac {3 b e^2 m n \text {Li}_2\left (-\frac {f x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )^2}{2 f^2}+\frac {3 b e^2 m n \log \left (\frac {f x}{e}+1\right ) \left (a+b \log \left (c x^n\right )\right )^2}{4 f^2}-\frac {e^2 m \log \left (\frac {f x}{e}+1\right ) \left (a+b \log \left (c x^n\right )\right )^3}{2 f^2}-\frac {9 b e m n x \left (a+b \log \left (c x^n\right )\right )^2}{4 f}+\frac {e m x \left (a+b \log \left (c x^n\right )\right )^3}{2 f}+\frac {3}{4} b m n x^2 \left (a+b \log \left (c x^n\right )\right )^2-\frac {1}{4} m x^2 \left (a+b \log \left (c x^n\right )\right )^3+\frac {21 b^3 e m n^2 x \log \left (c x^n\right )}{4 f}-\frac {3}{8} b^3 n^3 x^2 \log \left (d (e+f x)^m\right )-\frac {3 b^3 e^2 m n^3 \text {Li}_2\left (-\frac {f x}{e}\right )}{4 f^2}-\frac {3 b^3 e^2 m n^3 \text {Li}_3\left (-\frac {f x}{e}\right )}{2 f^2}-\frac {3 b^3 e^2 m n^3 \text {Li}_4\left (-\frac {f x}{e}\right )}{f^2}+\frac {3 b^3 e^2 m n^3 \log (e+f x)}{8 f^2}-\frac {45 b^3 e m n^3 x}{8 f}+\frac {3}{4} b^3 m n^3 x^2 \]
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Rubi [A] time = 0.97, antiderivative size = 603, normalized size of antiderivative = 1.00, number of steps used = 34, number of rules used = 13, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.542, Rules used = {2305, 2304, 2378, 43, 2351, 2295, 2317, 2391, 2353, 2296, 2374, 6589, 2383} \[ \frac {3 b^2 e^2 m n^2 \text {PolyLog}\left (2,-\frac {f x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )}{2 f^2}+\frac {3 b^2 e^2 m n^2 \text {PolyLog}\left (3,-\frac {f x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )}{f^2}-\frac {3 b e^2 m n \text {PolyLog}\left (2,-\frac {f x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )^2}{2 f^2}-\frac {3 b^3 e^2 m n^3 \text {PolyLog}\left (2,-\frac {f x}{e}\right )}{4 f^2}-\frac {3 b^3 e^2 m n^3 \text {PolyLog}\left (3,-\frac {f x}{e}\right )}{2 f^2}-\frac {3 b^3 e^2 m n^3 \text {PolyLog}\left (4,-\frac {f x}{e}\right )}{f^2}+\frac {3}{4} b^2 n^2 x^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (d (e+f x)^m\right )-\frac {3 b^2 e^2 m n^2 \log \left (\frac {f x}{e}+1\right ) \left (a+b \log \left (c x^n\right )\right )}{4 f^2}-\frac {9}{8} b^2 m n^2 x^2 \left (a+b \log \left (c x^n\right )\right )+\frac {21 a b^2 e m n^2 x}{4 f}-\frac {3}{4} b n x^2 \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+\frac {1}{2} x^2 \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )+\frac {3 b e^2 m n \log \left (\frac {f x}{e}+1\right ) \left (a+b \log \left (c x^n\right )\right )^2}{4 f^2}-\frac {e^2 m \log \left (\frac {f x}{e}+1\right ) \left (a+b \log \left (c x^n\right )\right )^3}{2 f^2}-\frac {9 b e m n x \left (a+b \log \left (c x^n\right )\right )^2}{4 f}+\frac {e m x \left (a+b \log \left (c x^n\right )\right )^3}{2 f}+\frac {3}{4} b m n x^2 \left (a+b \log \left (c x^n\right )\right )^2-\frac {1}{4} m x^2 \left (a+b \log \left (c x^n\right )\right )^3+\frac {21 b^3 e m n^2 x \log \left (c x^n\right )}{4 f}-\frac {3}{8} b^3 n^3 x^2 \log \left (d (e+f x)^m\right )+\frac {3 b^3 e^2 m n^3 \log (e+f x)}{8 f^2}-\frac {45 b^3 e m n^3 x}{8 f}+\frac {3}{4} b^3 m n^3 x^2 \]
Antiderivative was successfully verified.
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Rule 43
Rule 2295
Rule 2296
Rule 2304
Rule 2305
Rule 2317
Rule 2351
Rule 2353
Rule 2374
Rule 2378
Rule 2383
Rule 2391
Rule 6589
Rubi steps
\begin {align*} \int x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right ) \, dx &=-\frac {3}{8} b^3 n^3 x^2 \log \left (d (e+f x)^m\right )+\frac {3}{4} b^2 n^2 x^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (d (e+f x)^m\right )-\frac {3}{4} b n x^2 \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+\frac {1}{2} x^2 \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-(f m) \int \left (-\frac {3 b^3 n^3 x^2}{8 (e+f x)}+\frac {3 b^2 n^2 x^2 \left (a+b \log \left (c x^n\right )\right )}{4 (e+f x)}-\frac {3 b n x^2 \left (a+b \log \left (c x^n\right )\right )^2}{4 (e+f x)}+\frac {x^2 \left (a+b \log \left (c x^n\right )\right )^3}{2 (e+f x)}\right ) \, dx\\ &=-\frac {3}{8} b^3 n^3 x^2 \log \left (d (e+f x)^m\right )+\frac {3}{4} b^2 n^2 x^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (d (e+f x)^m\right )-\frac {3}{4} b n x^2 \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+\frac {1}{2} x^2 \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-\frac {1}{2} (f m) \int \frac {x^2 \left (a+b \log \left (c x^n\right )\right )^3}{e+f x} \, dx+\frac {1}{4} (3 b f m n) \int \frac {x^2 \left (a+b \log \left (c x^n\right )\right )^2}{e+f x} \, dx-\frac {1}{4} \left (3 b^2 f m n^2\right ) \int \frac {x^2 \left (a+b \log \left (c x^n\right )\right )}{e+f x} \, dx+\frac {1}{8} \left (3 b^3 f m n^3\right ) \int \frac {x^2}{e+f x} \, dx\\ &=-\frac {3}{8} b^3 n^3 x^2 \log \left (d (e+f x)^m\right )+\frac {3}{4} b^2 n^2 x^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (d (e+f x)^m\right )-\frac {3}{4} b n x^2 \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+\frac {1}{2} x^2 \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-\frac {1}{2} (f m) \int \left (-\frac {e \left (a+b \log \left (c x^n\right )\right )^3}{f^2}+\frac {x \left (a+b \log \left (c x^n\right )\right )^3}{f}+\frac {e^2 \left (a+b \log \left (c x^n\right )\right )^3}{f^2 (e+f x)}\right ) \, dx+\frac {1}{4} (3 b f m n) \int \left (-\frac {e \left (a+b \log \left (c x^n\right )\right )^2}{f^2}+\frac {x \left (a+b \log \left (c x^n\right )\right )^2}{f}+\frac {e^2 \left (a+b \log \left (c x^n\right )\right )^2}{f^2 (e+f x)}\right ) \, dx-\frac {1}{4} \left (3 b^2 f m n^2\right ) \int \left (-\frac {e \left (a+b \log \left (c x^n\right )\right )}{f^2}+\frac {x \left (a+b \log \left (c x^n\right )\right )}{f}+\frac {e^2 \left (a+b \log \left (c x^n\right )\right )}{f^2 (e+f x)}\right ) \, dx+\frac {1}{8} \left (3 b^3 f m n^3\right ) \int \left (-\frac {e}{f^2}+\frac {x}{f}+\frac {e^2}{f^2 (e+f x)}\right ) \, dx\\ &=-\frac {3 b^3 e m n^3 x}{8 f}+\frac {3}{16} b^3 m n^3 x^2+\frac {3 b^3 e^2 m n^3 \log (e+f x)}{8 f^2}-\frac {3}{8} b^3 n^3 x^2 \log \left (d (e+f x)^m\right )+\frac {3}{4} b^2 n^2 x^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (d (e+f x)^m\right )-\frac {3}{4} b n x^2 \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+\frac {1}{2} x^2 \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-\frac {1}{2} m \int x \left (a+b \log \left (c x^n\right )\right )^3 \, dx+\frac {(e m) \int \left (a+b \log \left (c x^n\right )\right )^3 \, dx}{2 f}-\frac {\left (e^2 m\right ) \int \frac {\left (a+b \log \left (c x^n\right )\right )^3}{e+f x} \, dx}{2 f}+\frac {1}{4} (3 b m n) \int x \left (a+b \log \left (c x^n\right )\right )^2 \, dx-\frac {(3 b e m n) \int \left (a+b \log \left (c x^n\right )\right )^2 \, dx}{4 f}+\frac {\left (3 b e^2 m n\right ) \int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{e+f x} \, dx}{4 f}-\frac {1}{4} \left (3 b^2 m n^2\right ) \int x \left (a+b \log \left (c x^n\right )\right ) \, dx+\frac {\left (3 b^2 e m n^2\right ) \int \left (a+b \log \left (c x^n\right )\right ) \, dx}{4 f}-\frac {\left (3 b^2 e^2 m n^2\right ) \int \frac {a+b \log \left (c x^n\right )}{e+f x} \, dx}{4 f}\\ &=\frac {3 a b^2 e m n^2 x}{4 f}-\frac {3 b^3 e m n^3 x}{8 f}+\frac {3}{8} b^3 m n^3 x^2-\frac {3}{8} b^2 m n^2 x^2 \left (a+b \log \left (c x^n\right )\right )-\frac {3 b e m n x \left (a+b \log \left (c x^n\right )\right )^2}{4 f}+\frac {3}{8} b m n x^2 \left (a+b \log \left (c x^n\right )\right )^2+\frac {e m x \left (a+b \log \left (c x^n\right )\right )^3}{2 f}-\frac {1}{4} m x^2 \left (a+b \log \left (c x^n\right )\right )^3+\frac {3 b^3 e^2 m n^3 \log (e+f x)}{8 f^2}-\frac {3}{8} b^3 n^3 x^2 \log \left (d (e+f x)^m\right )+\frac {3}{4} b^2 n^2 x^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (d (e+f x)^m\right )-\frac {3}{4} b n x^2 \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+\frac {1}{2} x^2 \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-\frac {3 b^2 e^2 m n^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (1+\frac {f x}{e}\right )}{4 f^2}+\frac {3 b e^2 m n \left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {f x}{e}\right )}{4 f^2}-\frac {e^2 m \left (a+b \log \left (c x^n\right )\right )^3 \log \left (1+\frac {f x}{e}\right )}{2 f^2}+\frac {1}{4} (3 b m n) \int x \left (a+b \log \left (c x^n\right )\right )^2 \, dx+\frac {\left (3 b e^2 m n\right ) \int \frac {\left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {f x}{e}\right )}{x} \, dx}{2 f^2}-\frac {(3 b e m n) \int \left (a+b \log \left (c x^n\right )\right )^2 \, dx}{2 f}-\frac {1}{4} \left (3 b^2 m n^2\right ) \int x \left (a+b \log \left (c x^n\right )\right ) \, dx-\frac {\left (3 b^2 e^2 m n^2\right ) \int \frac {\left (a+b \log \left (c x^n\right )\right ) \log \left (1+\frac {f x}{e}\right )}{x} \, dx}{2 f^2}+\frac {\left (3 b^2 e m n^2\right ) \int \left (a+b \log \left (c x^n\right )\right ) \, dx}{2 f}+\frac {\left (3 b^3 e m n^2\right ) \int \log \left (c x^n\right ) \, dx}{4 f}+\frac {\left (3 b^3 e^2 m n^3\right ) \int \frac {\log \left (1+\frac {f x}{e}\right )}{x} \, dx}{4 f^2}\\ &=\frac {9 a b^2 e m n^2 x}{4 f}-\frac {9 b^3 e m n^3 x}{8 f}+\frac {9}{16} b^3 m n^3 x^2+\frac {3 b^3 e m n^2 x \log \left (c x^n\right )}{4 f}-\frac {3}{4} b^2 m n^2 x^2 \left (a+b \log \left (c x^n\right )\right )-\frac {9 b e m n x \left (a+b \log \left (c x^n\right )\right )^2}{4 f}+\frac {3}{4} b m n x^2 \left (a+b \log \left (c x^n\right )\right )^2+\frac {e m x \left (a+b \log \left (c x^n\right )\right )^3}{2 f}-\frac {1}{4} m x^2 \left (a+b \log \left (c x^n\right )\right )^3+\frac {3 b^3 e^2 m n^3 \log (e+f x)}{8 f^2}-\frac {3}{8} b^3 n^3 x^2 \log \left (d (e+f x)^m\right )+\frac {3}{4} b^2 n^2 x^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (d (e+f x)^m\right )-\frac {3}{4} b n x^2 \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+\frac {1}{2} x^2 \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-\frac {3 b^2 e^2 m n^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (1+\frac {f x}{e}\right )}{4 f^2}+\frac {3 b e^2 m n \left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {f x}{e}\right )}{4 f^2}-\frac {e^2 m \left (a+b \log \left (c x^n\right )\right )^3 \log \left (1+\frac {f x}{e}\right )}{2 f^2}-\frac {3 b^3 e^2 m n^3 \text {Li}_2\left (-\frac {f x}{e}\right )}{4 f^2}+\frac {3 b^2 e^2 m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_2\left (-\frac {f x}{e}\right )}{2 f^2}-\frac {3 b e^2 m n \left (a+b \log \left (c x^n\right )\right )^2 \text {Li}_2\left (-\frac {f x}{e}\right )}{2 f^2}-\frac {1}{4} \left (3 b^2 m n^2\right ) \int x \left (a+b \log \left (c x^n\right )\right ) \, dx+\frac {\left (3 b^2 e^2 m n^2\right ) \int \frac {\left (a+b \log \left (c x^n\right )\right ) \text {Li}_2\left (-\frac {f x}{e}\right )}{x} \, dx}{f^2}+\frac {\left (3 b^2 e m n^2\right ) \int \left (a+b \log \left (c x^n\right )\right ) \, dx}{f}+\frac {\left (3 b^3 e m n^2\right ) \int \log \left (c x^n\right ) \, dx}{2 f}-\frac {\left (3 b^3 e^2 m n^3\right ) \int \frac {\text {Li}_2\left (-\frac {f x}{e}\right )}{x} \, dx}{2 f^2}\\ &=\frac {21 a b^2 e m n^2 x}{4 f}-\frac {21 b^3 e m n^3 x}{8 f}+\frac {3}{4} b^3 m n^3 x^2+\frac {9 b^3 e m n^2 x \log \left (c x^n\right )}{4 f}-\frac {9}{8} b^2 m n^2 x^2 \left (a+b \log \left (c x^n\right )\right )-\frac {9 b e m n x \left (a+b \log \left (c x^n\right )\right )^2}{4 f}+\frac {3}{4} b m n x^2 \left (a+b \log \left (c x^n\right )\right )^2+\frac {e m x \left (a+b \log \left (c x^n\right )\right )^3}{2 f}-\frac {1}{4} m x^2 \left (a+b \log \left (c x^n\right )\right )^3+\frac {3 b^3 e^2 m n^3 \log (e+f x)}{8 f^2}-\frac {3}{8} b^3 n^3 x^2 \log \left (d (e+f x)^m\right )+\frac {3}{4} b^2 n^2 x^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (d (e+f x)^m\right )-\frac {3}{4} b n x^2 \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+\frac {1}{2} x^2 \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-\frac {3 b^2 e^2 m n^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (1+\frac {f x}{e}\right )}{4 f^2}+\frac {3 b e^2 m n \left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {f x}{e}\right )}{4 f^2}-\frac {e^2 m \left (a+b \log \left (c x^n\right )\right )^3 \log \left (1+\frac {f x}{e}\right )}{2 f^2}-\frac {3 b^3 e^2 m n^3 \text {Li}_2\left (-\frac {f x}{e}\right )}{4 f^2}+\frac {3 b^2 e^2 m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_2\left (-\frac {f x}{e}\right )}{2 f^2}-\frac {3 b e^2 m n \left (a+b \log \left (c x^n\right )\right )^2 \text {Li}_2\left (-\frac {f x}{e}\right )}{2 f^2}-\frac {3 b^3 e^2 m n^3 \text {Li}_3\left (-\frac {f x}{e}\right )}{2 f^2}+\frac {3 b^2 e^2 m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_3\left (-\frac {f x}{e}\right )}{f^2}+\frac {\left (3 b^3 e m n^2\right ) \int \log \left (c x^n\right ) \, dx}{f}-\frac {\left (3 b^3 e^2 m n^3\right ) \int \frac {\text {Li}_3\left (-\frac {f x}{e}\right )}{x} \, dx}{f^2}\\ &=\frac {21 a b^2 e m n^2 x}{4 f}-\frac {45 b^3 e m n^3 x}{8 f}+\frac {3}{4} b^3 m n^3 x^2+\frac {21 b^3 e m n^2 x \log \left (c x^n\right )}{4 f}-\frac {9}{8} b^2 m n^2 x^2 \left (a+b \log \left (c x^n\right )\right )-\frac {9 b e m n x \left (a+b \log \left (c x^n\right )\right )^2}{4 f}+\frac {3}{4} b m n x^2 \left (a+b \log \left (c x^n\right )\right )^2+\frac {e m x \left (a+b \log \left (c x^n\right )\right )^3}{2 f}-\frac {1}{4} m x^2 \left (a+b \log \left (c x^n\right )\right )^3+\frac {3 b^3 e^2 m n^3 \log (e+f x)}{8 f^2}-\frac {3}{8} b^3 n^3 x^2 \log \left (d (e+f x)^m\right )+\frac {3}{4} b^2 n^2 x^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (d (e+f x)^m\right )-\frac {3}{4} b n x^2 \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+\frac {1}{2} x^2 \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-\frac {3 b^2 e^2 m n^2 \left (a+b \log \left (c x^n\right )\right ) \log \left (1+\frac {f x}{e}\right )}{4 f^2}+\frac {3 b e^2 m n \left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {f x}{e}\right )}{4 f^2}-\frac {e^2 m \left (a+b \log \left (c x^n\right )\right )^3 \log \left (1+\frac {f x}{e}\right )}{2 f^2}-\frac {3 b^3 e^2 m n^3 \text {Li}_2\left (-\frac {f x}{e}\right )}{4 f^2}+\frac {3 b^2 e^2 m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_2\left (-\frac {f x}{e}\right )}{2 f^2}-\frac {3 b e^2 m n \left (a+b \log \left (c x^n\right )\right )^2 \text {Li}_2\left (-\frac {f x}{e}\right )}{2 f^2}-\frac {3 b^3 e^2 m n^3 \text {Li}_3\left (-\frac {f x}{e}\right )}{2 f^2}+\frac {3 b^2 e^2 m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_3\left (-\frac {f x}{e}\right )}{f^2}-\frac {3 b^3 e^2 m n^3 \text {Li}_4\left (-\frac {f x}{e}\right )}{f^2}\\ \end {align*}
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Mathematica [B] time = 0.60, size = 1431, normalized size = 2.37 \[ \text {result too large to display} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.69, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (b^{3} x \log \left (c x^{n}\right )^{3} + 3 \, a b^{2} x \log \left (c x^{n}\right )^{2} + 3 \, a^{2} b x \log \left (c x^{n}\right ) + a^{3} x\right )} \log \left ({\left (f x + e\right )}^{m} d\right ), x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \log \left (c x^{n}\right ) + a\right )}^{3} x \log \left ({\left (f x + e\right )}^{m} d\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 87.77, size = 0, normalized size = 0.00 \[ \int \left (b \ln \left (c \,x^{n}\right )+a \right )^{3} x \ln \left (d \left (f x +e \right )^{m}\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int x\,\ln \left (d\,{\left (e+f\,x\right )}^m\right )\,{\left (a+b\,\ln \left (c\,x^n\right )\right )}^3 \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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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.
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