- #1

ShayanJ

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## Main Question or Discussion Point

I wanna calculate the integral [itex] \int_0^{\infty} \frac{x^a}{(1+x)^2}dx \ (-1<a<1) [/itex] via contour integration But it seems a little tricky.

I tried to solve it like example4 in the page ( http://en.wikipedia.org/wiki/Contour_integral#Example_.28IV.29_.E2.80.93_branch_cuts ) but I arrived at zero which I know is wrong.(The answer is [itex] \frac{\pi a}{\sin{\pi a}} [/itex])What's the point?

Thanks

I tried to solve it like example4 in the page ( http://en.wikipedia.org/wiki/Contour_integral#Example_.28IV.29_.E2.80.93_branch_cuts ) but I arrived at zero which I know is wrong.(The answer is [itex] \frac{\pi a}{\sin{\pi a}} [/itex])What's the point?

Thanks