Need to evaluate
int(0,inf)((x^(a-1))/(1-x))dx by contour integration and the residue theorem, where a < 1. The solution is pi*cot((a-1)*pi). I'm not sure how to choose the contour to integrate around.
The Attempt at a Solution
Performing a complex integral, the function has singularities at z=0 and z=1. I am under the impression we want to avoid singularities on the real line, so I'm guessing I need some sort of double keyhole contour... but I'm not sure. Any help would be much appreciated.