\[ \int \frac {\text {PolyLog}(2,x)}{(-1+x) x} \, dx \]
Optimal antiderivative \[ \ln \left (1-x \right )^{2} \ln \left (x \right )+2 \ln \left (1-x \right ) \polylog \left (2, 1-x \right )+\ln \left (1-x \right ) \polylog \left (2, x\right )-2 \polylog \left (3, 1-x \right )-\polylog \left (3, x\right ) \]
command
int(polylog(2,x)/(-1+x)/x,x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(\ln \left (-1+x \right ) \polylog \left (2, x\right )+\ln \left (-1+x \right )^{2} \ln \left (x \right )+2 \ln \left (-1+x \right ) \polylog \left (2, 1-x \right )-2 \polylog \left (3, 1-x \right )+\ln \left (x \right ) \ln \left (-1+x \right ) \left (\ln \left (1-x \right )-\ln \left (-1+x \right )\right )+\dilog \left (x \right ) \left (\ln \left (1-x \right )-\ln \left (-1+x \right )\right )-\polylog \left (3, x\right )\) | \(82\) |
Maple 2021.1 output
\[ \int \frac {\polylog \left (2, x\right )}{\left (-1+x \right ) x}\, dx \]________________________________________________________________________________________