\[ \int \frac {\tan ^{-1}(x) \log (x)}{x} \, dx \]
Optimal antiderivative \[ \frac {i \ln \left (x \right ) \polylog \left (2, -i x \right )}{2}-\frac {i \ln \left (x \right ) \polylog \left (2, i x \right )}{2}-\frac {i \polylog \left (3, -i x \right )}{2}+\frac {i \polylog \left (3, i x \right )}{2} \]
command
int(arctan(x)*ln(x)/x,x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\frac {i \ln \left (x \right )^{2} \ln \left (-i \left (x +i\right )\right )}{4}-\frac {i \ln \left (x \right )^{2} \ln \left (-i x +1\right )}{4}-\frac {i \ln \left (x \right ) \polylog \left (2, i x \right )}{2}+\frac {i \polylog \left (3, i x \right )}{2}+\frac {i \ln \left (x \right ) \polylog \left (2, -i x \right )}{2}-\frac {i \polylog \left (3, -i x \right )}{2}\) | \(71\) |
Maple 2021.1 output
\[ \int \frac {\arctan \left (x \right ) \ln \left (x \right )}{x}\, dx \]________________________________________________________________________________________