This question is similar to another one I've posted

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so I let

And I used a closed semicircle which contains of radius R.

Let

I let: and

By Jordan's Lemma, as

By the Cauchy Residue Theorem

Now I use the following theorem to evaluate the theorem

If is entire and is analytic everywhere except but is entire.

The

However, I can't get the following to evaluate correctly

I am having troubles with . None of the identities in my text book seem to help.