\[ \int \frac {\left (a+b \tanh ^{-1}(c x)\right )^3}{d+e x} \, dx \]
Optimal antiderivative \[ -\frac {\left (a +b \arctanh \left (c x \right )\right )^{3} \ln \left (\frac {2}{c x +1}\right )}{e}+\frac {\left (a +b \arctanh \left (c x \right )\right )^{3} \ln \left (\frac {2 c \left (e x +d \right )}{\left (c d +e \right ) \left (c x +1\right )}\right )}{e}+\frac {3 b \left (a +b \arctanh \left (c x \right )\right )^{2} \polylog \left (2, 1-\frac {2}{c x +1}\right )}{2 e}-\frac {3 b \left (a +b \arctanh \left (c x \right )\right )^{2} \polylog \left (2, 1-\frac {2 c \left (e x +d \right )}{\left (c d +e \right ) \left (c x +1\right )}\right )}{2 e}+\frac {3 b^{2} \left (a +b \arctanh \left (c x \right )\right ) \polylog \left (3, 1-\frac {2}{c x +1}\right )}{2 e}-\frac {3 b^{2} \left (a +b \arctanh \left (c x \right )\right ) \polylog \left (3, 1-\frac {2 c \left (e x +d \right )}{\left (c d +e \right ) \left (c x +1\right )}\right )}{2 e}+\frac {3 b^{3} \polylog \left (4, 1-\frac {2}{c x +1}\right )}{4 e}-\frac {3 b^{3} \polylog \left (4, 1-\frac {2 c \left (e x +d \right )}{\left (c d +e \right ) \left (c x +1\right )}\right )}{4 e} \]
command
Integrate[(a + b*ArcTanh[c*x])^3/(d + e*x),x]
Mathematica 13.1 output
\[ \text {Result too large to show} \]
Mathematica 12.3 output
\[ \int \frac {\left (a+b \tanh ^{-1}(c x)\right )^3}{d+e x} \, dx \]________________________________________________________________________________________