\[ \int -\frac {\text {PolyLog}(2,x)}{1-x} \, dx \]
Optimal antiderivative \[ \ln \left (1-x \right )^{2} \ln \left (x \right )+2 \ln \left (1-x \right ) \polylog \left (2, 1-x \right )+\ln \left (1-x \right ) \polylog \left (2, x\right )-2 \polylog \left (3, 1-x \right ) \]
command
int(-polylog(2,x)/(1-x),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(\ln \left (-1+x \right ) \polylog \left (2, x\right )+\ln \left (1-x \right )^{2} \ln \left (x \right )+2 \ln \left (1-x \right ) \polylog \left (2, 1-x \right )-2 \polylog \left (3, 1-x \right )-\left (\ln \left (-1+x \right )-\ln \left (1-x \right )\right ) \dilog \left (1-x \right )\) | \(66\) |
Maple 2021.1 output
\[ \int -\frac {\polylog \left (2, x\right )}{1-x}\, dx \]________________________________________________________________________________________