\[ \int \frac {\text {PolyLog}(2,x)}{-1+x} \, dx \]
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
integrate(polylog(2,x)/(-1+x),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \log \left (x\right ) \log \left (-x + 1\right )^{2} + {\left ({\rm Li}_2\left (x\right ) + 2 \, {\rm Li}_2\left (-x + 1\right )\right )} \log \left (-x + 1\right ) - 2 \, {\rm polylog}\left (3, -x + 1\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\rm Li}_2\left (x\right )}{x - 1}, x\right ) \]