Hey, I was wondering if anyone managed to solve problem 53 on the practice test GR9768? The problem is:

In the complex plane, let C be the circle |z|=2 with positive (counterclockwise) orientation. Then the line integral of a scalar-valued function 1/((z-1)*(z+3)^2) over path C is

(A) 0

(B) 2*pi*i

(C) (pi*i)/2

(D) (pi*i)/8

(E) (pi*1)/16

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The answer is supposed to be (D), however after several attempts I continue to get (A).

Could someone possible show the first one or two steps of this problem? Don't worry about writing the whole thing out. Thanks!