\[ \int \log \left (a \cot ^n(x)\right ) \, dx \]
Optimal antiderivative \[ -2 n x \arctanh \left ({\mathrm e}^{2 i x}\right )+x \ln \left (a \left (\cot ^{n}\left (x \right )\right )\right )+\frac {i n \polylog \left (2, -{\mathrm e}^{2 i x}\right )}{2}-\frac {i n \polylog \left (2, {\mathrm e}^{2 i x}\right )}{2} \]
command
int(ln(a*cot(x)^n),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(2357\) |
Maple 2021.1 output
\[ \int \ln \left (a \left (\cot ^{n}\left (x \right )\right )\right )\, dx \]________________________________________________________________________________________