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## Homework Statement

[tex]\int_{|z| = 2} \sqrt{z^2 - 1}[/tex]

## Homework Equations

[tex]\sqrt{z^2 - 1} = e^{\frac{1}{2} log(z+1) + \frac{1}{2} log(z - 1)}[/tex]

## The Attempt at a Solution

Honestly, my only thoughts are expanding this as some hideous Taylor series and integrating term by term. But I know there has to be a simpler way to go about it. I tried to find an antiderivative (with a little Calculus 2 cheating), but I got [itex]\frac{1}{2}(z\sqrt{z^2 - 1} - log(z + \sqrt{z^2 - 1}))[/itex], which may or may not be correct (I took the derivative, saw the horrendous expression that came out, and my brain immediately shut down). But even if it is, choosing an appropriate branch for the log function seems like it would be kind of tricky.

Anyway, suggestions would be appreciated. Thanks.