I am trying to determine if Cauchy's integral formula will work on the following integral, where the contour C is the unit circle traversed in the counterclockwise direction.
See Cauchy's Integral Formula - http://en.wikipedia.org/wiki/Cauchy_integral_formula" [Broken]
The Attempt at a Solution
I realize that there is a pole at z=0. I realize that if I could get this integral into the form
with f(z) being analytic in and on the contour C, then I could use the formula. However, I'm not sure how to get the integrand in that form. Is it even possible to use Cauchy's integral formula on this integral, or do I need to use a different method to evaluate this integral?
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