Mathematics GRE

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!

Are you using the Residue Theorem?
Notice that we have one (simple) pole at z = 1 within the circle.
So, we can say the value of the integral is 2*Pi*i*Res(f,1) = 2*Pi*i*(1/16).

Thanks!