\[ \int \frac {\left (a+b \log \left (c x^n\right )\right )^3 \log (1+e x)}{x} \, dx \]
Optimal antiderivative \[ -\left (a +b \ln \left (c \,x^{n}\right )\right )^{3} \polylog \left (2, -e x \right )+3 b n \left (a +b \ln \left (c \,x^{n}\right )\right )^{2} \polylog \left (3, -e x \right )-6 b^{2} n^{2} \left (a +b \ln \left (c \,x^{n}\right )\right ) \polylog \left (4, -e x \right )+6 b^{3} n^{3} \polylog \left (5, -e x \right ) \]
command
int((a+b*ln(c*x^n))^3*ln(e*x+1)/x,x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(4058\) |
Maple 2021.1 output
\[ \int \frac {\left (b \ln \left (c \,x^{n}\right )+a \right )^{3} \ln \left (e x +1\right )}{x}\, dx \]________________________________________________________________________________________