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## Homework Statement

## The Attempt at a Solution

We can parametrise the contour [itex]\gamma[/itex] (the positively oriented unit circle) by [itex]\gamma(t) = e^{it}[/itex] for [itex]t \in [0, 2\pi ][/itex]

So by the definition of a contour integral

[itex]\displaystyle I = \frac{1}{2\pi i} \int^{2\pi}_0 \frac{2e^{it}}{e^{2it} + w^2} ie^{it} \; dt[/itex]

[itex]\displaystyle \;\;\;= \frac{1}{\pi} \int^{2\pi}_0 \frac{e^{2it}}{e^{2it} + w^2} \; dt[/itex]

How do I evaluate this?