Optimal. Leaf size=473 \[ -12 a b^2 m n^2 x+18 b^3 m n^3 x-6 b^2 m n^2 (a-b n) x-18 b^3 m n^2 x \log \left (c x^n\right )+6 b m n x \left (a+b \log \left (c x^n\right )\right )^2-m x \left (a+b \log \left (c x^n\right )\right )^3+\frac {6 b^2 e m n^2 (a-b n) \log (e+f x)}{f}+6 a b^2 n^2 x \log \left (d (e+f x)^m\right )-6 b^3 n^3 x \log \left (d (e+f x)^m\right )+6 b^3 n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )-3 b n x \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )+\frac {6 b^3 e m n^2 \log \left (c x^n\right ) \log \left (1+\frac {f x}{e}\right )}{f}-\frac {3 b e m n \left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {f x}{e}\right )}{f}+\frac {e m \left (a+b \log \left (c x^n\right )\right )^3 \log \left (1+\frac {f x}{e}\right )}{f}+\frac {6 b^3 e m n^3 \text {Li}_2\left (-\frac {f x}{e}\right )}{f}-\frac {6 b^2 e m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_2\left (-\frac {f x}{e}\right )}{f}+\frac {3 b e m n \left (a+b \log \left (c x^n\right )\right )^2 \text {Li}_2\left (-\frac {f x}{e}\right )}{f}+\frac {6 b^3 e m n^3 \text {Li}_3\left (-\frac {f x}{e}\right )}{f}-\frac {6 b^2 e m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_3\left (-\frac {f x}{e}\right )}{f}+\frac {6 b^3 e m n^3 \text {Li}_4\left (-\frac {f x}{e}\right )}{f} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.43, antiderivative size = 473, normalized size of antiderivative = 1.00, number of steps
used = 28, number of rules used = 12, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.522, Rules used = {2333, 2332,
2418, 6, 45, 2393, 2354, 2438, 2395, 2421, 6724, 2430} \begin {gather*} -\frac {6 b^2 e m n^2 \text {PolyLog}\left (2,-\frac {f x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )}{f}-\frac {6 b^2 e m n^2 \text {PolyLog}\left (3,-\frac {f x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )}{f}+\frac {3 b e m n \text {PolyLog}\left (2,-\frac {f x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )^2}{f}+\frac {6 b^3 e m n^3 \text {PolyLog}\left (2,-\frac {f x}{e}\right )}{f}+\frac {6 b^3 e m n^3 \text {PolyLog}\left (3,-\frac {f x}{e}\right )}{f}+\frac {6 b^3 e m n^3 \text {PolyLog}\left (4,-\frac {f x}{e}\right )}{f}+6 a b^2 n^2 x \log \left (d (e+f x)^m\right )+\frac {6 b^2 e m n^2 (a-b n) \log (e+f x)}{f}-12 a b^2 m n^2 x-6 b^2 m n^2 x (a-b n)-3 b n x \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-\frac {3 b e m n \log \left (\frac {f x}{e}+1\right ) \left (a+b \log \left (c x^n\right )\right )^2}{f}+\frac {e m \log \left (\frac {f x}{e}+1\right ) \left (a+b \log \left (c x^n\right )\right )^3}{f}+6 b m n x \left (a+b \log \left (c x^n\right )\right )^2-m x \left (a+b \log \left (c x^n\right )\right )^3+6 b^3 n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )+\frac {6 b^3 e m n^2 \log \left (c x^n\right ) \log \left (\frac {f x}{e}+1\right )}{f}-18 b^3 m n^2 x \log \left (c x^n\right )-6 b^3 n^3 x \log \left (d (e+f x)^m\right )+18 b^3 m n^3 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 45
Rule 2332
Rule 2333
Rule 2354
Rule 2393
Rule 2395
Rule 2418
Rule 2421
Rule 2430
Rule 2438
Rule 6724
Rubi steps
\begin {align*} \int \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right ) \, dx &=6 a b^2 n^2 x \log \left (d (e+f x)^m\right )-6 b^3 n^3 x \log \left (d (e+f x)^m\right )+6 b^3 n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )-3 b n x \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-(f m) \int \left (\frac {6 a b^2 n^2 x}{e+f x}-\frac {6 b^3 n^3 x}{e+f x}+\frac {6 b^3 n^2 x \log \left (c x^n\right )}{e+f x}-\frac {3 b n x \left (a+b \log \left (c x^n\right )\right )^2}{e+f x}+\frac {x \left (a+b \log \left (c x^n\right )\right )^3}{e+f x}\right ) \, dx\\ &=6 a b^2 n^2 x \log \left (d (e+f x)^m\right )-6 b^3 n^3 x \log \left (d (e+f x)^m\right )+6 b^3 n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )-3 b n x \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-(f m) \int \left (\frac {\left (6 a b^2 n^2-6 b^3 n^3\right ) x}{e+f x}+\frac {6 b^3 n^2 x \log \left (c x^n\right )}{e+f x}-\frac {3 b n x \left (a+b \log \left (c x^n\right )\right )^2}{e+f x}+\frac {x \left (a+b \log \left (c x^n\right )\right )^3}{e+f x}\right ) \, dx\\ &=6 a b^2 n^2 x \log \left (d (e+f x)^m\right )-6 b^3 n^3 x \log \left (d (e+f x)^m\right )+6 b^3 n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )-3 b n x \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-(f m) \int \frac {x \left (a+b \log \left (c x^n\right )\right )^3}{e+f x} \, dx+(3 b f m n) \int \frac {x \left (a+b \log \left (c x^n\right )\right )^2}{e+f x} \, dx-\left (6 b^3 f m n^2\right ) \int \frac {x \log \left (c x^n\right )}{e+f x} \, dx-\left (6 b^2 f m n^2 (a-b n)\right ) \int \frac {x}{e+f x} \, dx\\ &=6 a b^2 n^2 x \log \left (d (e+f x)^m\right )-6 b^3 n^3 x \log \left (d (e+f x)^m\right )+6 b^3 n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )-3 b n x \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-(f m) \int \left (\frac {\left (a+b \log \left (c x^n\right )\right )^3}{f}-\frac {e \left (a+b \log \left (c x^n\right )\right )^3}{f (e+f x)}\right ) \, dx+(3 b f m n) \int \left (\frac {\left (a+b \log \left (c x^n\right )\right )^2}{f}-\frac {e \left (a+b \log \left (c x^n\right )\right )^2}{f (e+f x)}\right ) \, dx-\left (6 b^3 f m n^2\right ) \int \left (\frac {\log \left (c x^n\right )}{f}-\frac {e \log \left (c x^n\right )}{f (e+f x)}\right ) \, dx-\left (6 b^2 f m n^2 (a-b n)\right ) \int \left (\frac {1}{f}-\frac {e}{f (e+f x)}\right ) \, dx\\ &=-6 b^2 m n^2 (a-b n) x+\frac {6 b^2 e m n^2 (a-b n) \log (e+f x)}{f}+6 a b^2 n^2 x \log \left (d (e+f x)^m\right )-6 b^3 n^3 x \log \left (d (e+f x)^m\right )+6 b^3 n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )-3 b n x \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )-m \int \left (a+b \log \left (c x^n\right )\right )^3 \, dx+(e m) \int \frac {\left (a+b \log \left (c x^n\right )\right )^3}{e+f x} \, dx+(3 b m n) \int \left (a+b \log \left (c x^n\right )\right )^2 \, dx-(3 b e m n) \int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{e+f x} \, dx-\left (6 b^3 m n^2\right ) \int \log \left (c x^n\right ) \, dx+\left (6 b^3 e m n^2\right ) \int \frac {\log \left (c x^n\right )}{e+f x} \, dx\\ &=6 b^3 m n^3 x-6 b^2 m n^2 (a-b n) x-6 b^3 m n^2 x \log \left (c x^n\right )+3 b m n x \left (a+b \log \left (c x^n\right )\right )^2-m x \left (a+b \log \left (c x^n\right )\right )^3+\frac {6 b^2 e m n^2 (a-b n) \log (e+f x)}{f}+6 a b^2 n^2 x \log \left (d (e+f x)^m\right )-6 b^3 n^3 x \log \left (d (e+f x)^m\right )+6 b^3 n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )-3 b n x \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )+\frac {6 b^3 e m n^2 \log \left (c x^n\right ) \log \left (1+\frac {f x}{e}\right )}{f}-\frac {3 b e m n \left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {f x}{e}\right )}{f}+\frac {e m \left (a+b \log \left (c x^n\right )\right )^3 \log \left (1+\frac {f x}{e}\right )}{f}+(3 b m n) \int \left (a+b \log \left (c x^n\right )\right )^2 \, dx-\frac {(3 b e m n) \int \frac {\left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {f x}{e}\right )}{x} \, dx}{f}-\left (6 b^2 m n^2\right ) \int \left (a+b \log \left (c x^n\right )\right ) \, dx+\frac {\left (6 b^2 e 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}{f}-\frac {\left (6 b^3 e m n^3\right ) \int \frac {\log \left (1+\frac {f x}{e}\right )}{x} \, dx}{f}\\ &=-6 a b^2 m n^2 x+6 b^3 m n^3 x-6 b^2 m n^2 (a-b n) x-6 b^3 m n^2 x \log \left (c x^n\right )+6 b m n x \left (a+b \log \left (c x^n\right )\right )^2-m x \left (a+b \log \left (c x^n\right )\right )^3+\frac {6 b^2 e m n^2 (a-b n) \log (e+f x)}{f}+6 a b^2 n^2 x \log \left (d (e+f x)^m\right )-6 b^3 n^3 x \log \left (d (e+f x)^m\right )+6 b^3 n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )-3 b n x \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )+\frac {6 b^3 e m n^2 \log \left (c x^n\right ) \log \left (1+\frac {f x}{e}\right )}{f}-\frac {3 b e m n \left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {f x}{e}\right )}{f}+\frac {e m \left (a+b \log \left (c x^n\right )\right )^3 \log \left (1+\frac {f x}{e}\right )}{f}+\frac {6 b^3 e m n^3 \text {Li}_2\left (-\frac {f x}{e}\right )}{f}-\frac {6 b^2 e m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_2\left (-\frac {f x}{e}\right )}{f}+\frac {3 b e m n \left (a+b \log \left (c x^n\right )\right )^2 \text {Li}_2\left (-\frac {f x}{e}\right )}{f}-\left (6 b^2 m n^2\right ) \int \left (a+b \log \left (c x^n\right )\right ) \, dx-\left (6 b^3 m n^2\right ) \int \log \left (c x^n\right ) \, dx-\frac {\left (6 b^2 e 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}+\frac {\left (6 b^3 e m n^3\right ) \int \frac {\text {Li}_2\left (-\frac {f x}{e}\right )}{x} \, dx}{f}\\ &=-12 a b^2 m n^2 x+12 b^3 m n^3 x-6 b^2 m n^2 (a-b n) x-12 b^3 m n^2 x \log \left (c x^n\right )+6 b m n x \left (a+b \log \left (c x^n\right )\right )^2-m x \left (a+b \log \left (c x^n\right )\right )^3+\frac {6 b^2 e m n^2 (a-b n) \log (e+f x)}{f}+6 a b^2 n^2 x \log \left (d (e+f x)^m\right )-6 b^3 n^3 x \log \left (d (e+f x)^m\right )+6 b^3 n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )-3 b n x \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )+\frac {6 b^3 e m n^2 \log \left (c x^n\right ) \log \left (1+\frac {f x}{e}\right )}{f}-\frac {3 b e m n \left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {f x}{e}\right )}{f}+\frac {e m \left (a+b \log \left (c x^n\right )\right )^3 \log \left (1+\frac {f x}{e}\right )}{f}+\frac {6 b^3 e m n^3 \text {Li}_2\left (-\frac {f x}{e}\right )}{f}-\frac {6 b^2 e m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_2\left (-\frac {f x}{e}\right )}{f}+\frac {3 b e m n \left (a+b \log \left (c x^n\right )\right )^2 \text {Li}_2\left (-\frac {f x}{e}\right )}{f}+\frac {6 b^3 e m n^3 \text {Li}_3\left (-\frac {f x}{e}\right )}{f}-\frac {6 b^2 e m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_3\left (-\frac {f x}{e}\right )}{f}-\left (6 b^3 m n^2\right ) \int \log \left (c x^n\right ) \, dx+\frac {\left (6 b^3 e m n^3\right ) \int \frac {\text {Li}_3\left (-\frac {f x}{e}\right )}{x} \, dx}{f}\\ &=-12 a b^2 m n^2 x+18 b^3 m n^3 x-6 b^2 m n^2 (a-b n) x-18 b^3 m n^2 x \log \left (c x^n\right )+6 b m n x \left (a+b \log \left (c x^n\right )\right )^2-m x \left (a+b \log \left (c x^n\right )\right )^3+\frac {6 b^2 e m n^2 (a-b n) \log (e+f x)}{f}+6 a b^2 n^2 x \log \left (d (e+f x)^m\right )-6 b^3 n^3 x \log \left (d (e+f x)^m\right )+6 b^3 n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )-3 b n x \left (a+b \log \left (c x^n\right )\right )^2 \log \left (d (e+f x)^m\right )+x \left (a+b \log \left (c x^n\right )\right )^3 \log \left (d (e+f x)^m\right )+\frac {6 b^3 e m n^2 \log \left (c x^n\right ) \log \left (1+\frac {f x}{e}\right )}{f}-\frac {3 b e m n \left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {f x}{e}\right )}{f}+\frac {e m \left (a+b \log \left (c x^n\right )\right )^3 \log \left (1+\frac {f x}{e}\right )}{f}+\frac {6 b^3 e m n^3 \text {Li}_2\left (-\frac {f x}{e}\right )}{f}-\frac {6 b^2 e m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_2\left (-\frac {f x}{e}\right )}{f}+\frac {3 b e m n \left (a+b \log \left (c x^n\right )\right )^2 \text {Li}_2\left (-\frac {f x}{e}\right )}{f}+\frac {6 b^3 e m n^3 \text {Li}_3\left (-\frac {f x}{e}\right )}{f}-\frac {6 b^2 e m n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_3\left (-\frac {f x}{e}\right )}{f}+\frac {6 b^3 e m n^3 \text {Li}_4\left (-\frac {f x}{e}\right )}{f}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1122\) vs. \(2(473)=946\).
time = 0.26, size = 1122, normalized size = 2.37 \begin {gather*} \frac {-a^3 f m x+6 a^2 b f m n x-18 a b^2 f m n^2 x+24 b^3 f m n^3 x-3 a^2 b f m x \log \left (c x^n\right )+12 a b^2 f m n x \log \left (c x^n\right )-18 b^3 f m n^2 x \log \left (c x^n\right )-3 a b^2 f m x \log ^2\left (c x^n\right )+6 b^3 f m n x \log ^2\left (c x^n\right )-b^3 f m x \log ^3\left (c x^n\right )+a^3 e m \log (e+f x)-3 a^2 b e m n \log (e+f x)+6 a b^2 e m n^2 \log (e+f x)-6 b^3 e m n^3 \log (e+f x)-3 a^2 b e m n \log (x) \log (e+f x)+6 a b^2 e m n^2 \log (x) \log (e+f x)-6 b^3 e m n^3 \log (x) \log (e+f x)+3 a b^2 e m n^2 \log ^2(x) \log (e+f x)-3 b^3 e m n^3 \log ^2(x) \log (e+f x)-b^3 e m n^3 \log ^3(x) \log (e+f x)+3 a^2 b e m \log \left (c x^n\right ) \log (e+f x)-6 a b^2 e m n \log \left (c x^n\right ) \log (e+f x)+6 b^3 e m n^2 \log \left (c x^n\right ) \log (e+f x)-6 a b^2 e m n \log (x) \log \left (c x^n\right ) \log (e+f x)+6 b^3 e m n^2 \log (x) \log \left (c x^n\right ) \log (e+f x)+3 b^3 e m n^2 \log ^2(x) \log \left (c x^n\right ) \log (e+f x)+3 a b^2 e m \log ^2\left (c x^n\right ) \log (e+f x)-3 b^3 e m n \log ^2\left (c x^n\right ) \log (e+f x)-3 b^3 e m n \log (x) \log ^2\left (c x^n\right ) \log (e+f x)+b^3 e m \log ^3\left (c x^n\right ) \log (e+f x)+a^3 f x \log \left (d (e+f x)^m\right )-3 a^2 b f n x \log \left (d (e+f x)^m\right )+6 a b^2 f n^2 x \log \left (d (e+f x)^m\right )-6 b^3 f n^3 x \log \left (d (e+f x)^m\right )+3 a^2 b f x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )-6 a b^2 f n x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )+6 b^3 f n^2 x \log \left (c x^n\right ) \log \left (d (e+f x)^m\right )+3 a b^2 f x \log ^2\left (c x^n\right ) \log \left (d (e+f x)^m\right )-3 b^3 f n x \log ^2\left (c x^n\right ) \log \left (d (e+f x)^m\right )+b^3 f x \log ^3\left (c x^n\right ) \log \left (d (e+f x)^m\right )+3 a^2 b e m n \log (x) \log \left (1+\frac {f x}{e}\right )-6 a b^2 e m n^2 \log (x) \log \left (1+\frac {f x}{e}\right )+6 b^3 e m n^3 \log (x) \log \left (1+\frac {f x}{e}\right )-3 a b^2 e m n^2 \log ^2(x) \log \left (1+\frac {f x}{e}\right )+3 b^3 e m n^3 \log ^2(x) \log \left (1+\frac {f x}{e}\right )+b^3 e m n^3 \log ^3(x) \log \left (1+\frac {f x}{e}\right )+6 a b^2 e m n \log (x) \log \left (c x^n\right ) \log \left (1+\frac {f x}{e}\right )-6 b^3 e m n^2 \log (x) \log \left (c x^n\right ) \log \left (1+\frac {f x}{e}\right )-3 b^3 e m n^2 \log ^2(x) \log \left (c x^n\right ) \log \left (1+\frac {f x}{e}\right )+3 b^3 e m n \log (x) \log ^2\left (c x^n\right ) \log \left (1+\frac {f x}{e}\right )+3 b e m n \left (a^2-2 a b n+2 b^2 n^2+2 b (a-b n) \log \left (c x^n\right )+b^2 \log ^2\left (c x^n\right )\right ) \text {Li}_2\left (-\frac {f x}{e}\right )-6 b^2 e m n^2 \left (a-b n+b \log \left (c x^n\right )\right ) \text {Li}_3\left (-\frac {f x}{e}\right )+6 b^3 e m n^3 \text {Li}_4\left (-\frac {f x}{e}\right )}{f} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
4.
time = 1.10, size = 39644, normalized size = 83.81
method | result | size |
risch | \(\text {Expression too large to display}\) | \(39644\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [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]
________________________________________________________________________________________
Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \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 \ln \left (d\,{\left (e+f\,x\right )}^m\right )\,{\left (a+b\,\ln \left (c\,x^n\right )\right )}^3 \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________