\[ \int \log \left (a \tan ^n(x)\right ) \, dx \]
Optimal antiderivative \[ 2 n x \arctanh \left ({\mathrm e}^{2 i x}\right )+x \ln \left (a \left (\tan ^{n}\left (x \right )\right )\right )-\frac {i n \polylog \left (2, -{\mathrm e}^{2 i x}\right )}{2}+\frac {i n \polylog \left (2, {\mathrm e}^{2 i x}\right )}{2} \]
command
int(ln(a*tan(x)^n),x,method=_RETURNVERBOSE)
Maple 2022.1 output
method | result | size |
risch | \(\text {Expression too large to display}\) | \(2356\) |
Maple 2021.1 output
\[ \int \ln \left (a \left (\tan ^{n}\left (x \right )\right )\right )\, dx \]________________________________________________________________________________________