I need to evaluate $\int_0^1 \frac{\log(x)}{1−x}\;dx$
I know I need to use contour integration and I read the chapter in Churchill but I'm still running into issues doing it properly.
I also know the answer is $\displaystyle\;\; −\frac{\pi^2}{6},$ but I'd like to know how to arrive at that answer.
Thanks!