Determine the value of ∫01ln(x)1−xdx\int_0^1 \frac{\ln(x)}{1-x} dx∫011−xln(x)dx.
−π26-\frac{\pi^2}{6}−6π2
−π23-\frac{\pi^2}{3}−3π2
π26\frac{\pi^2}{6}6π2
π212\frac{\pi^2}{12}12π2