Contour integral

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NT123
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Homework Statement

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.



Homework Equations





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.
 

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