REPOST** Evaluating an integral with pole of order 2

Earlier today I posted the problem below, and received a response which was great but it is not done in the manner that our professor wants it done. He wants us to use the branch cut of the negative Im axis, and use the following curve: C= -R to R, -p to p, p to R, and Cr from 0 to pi. Can anyone do this problem using these parameters? Original posting: Problem: Evaluate the integral from 0 to INF of: (x^a)/(x^2 +4)^2 dx, -1 < a < 3 We are to use f(z)= (z^a)/(z^2 +4)^2, with z^a = e^(a Log z), Log z= ln|z| + i Arg z, and -pi/2 < Arg z < 3pi/2. I have found the residue at 2i to be: [2^a(1-a)/16]*[cos ((pi*a)/2) + i sin ((pi*a)/2). Please let me know if this is correct and how to ... click for more

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