Procedure to find Cauchy Integral

[DrMath]

Homework Statement

I have a question - just to check when we know the whole function is not analytic at some point of z. We can use cauchy integral formula of 2*pi*j*f(a) to find the answer.

In between; one of such method is to use Partial Fraction to break up the rational functions.
So do we have to take out the numerator (which is analytic before doing the Integral?).

Homework Equations

The Attempt at a Solution

 

[jmb]

It's very hard to work out from what you say what your question is, I'm afraid!. If you are talking about using the residue theorem to evaluate a contour integral of a function that is basically a fraction with a pole at some point (within the contour), then the answer is that you don't need to take out the denominator of the fraction before evaluating the answer as its effect will just be included in the evaluation of the residue.