Q: Evaluate , where is the circle of raduis 1 centered at 2 traveled once conterclockwise.

First thing I did was use partial fraction decomp to break up the integrand. I ended up with

traveled counter clockwise. So, I can let and for . This gives the parametrisized equation

.

From here I am not entirely sure what I should do. I tried breaking the integral up into is real and imaginary components and using greens thereom, but that seems like too much. I would like to use the fundamental thereom of contour integrals, but the integrand is not defined on at 2, so I don't think I can use it.

Doing it the way I just mentioned I ended up with 0 as my answer.

Thanks