# Use Cauchy Integral Formula to evaluate the integral

## Homework Statement

The question is needed to be done by using an appropriate substitution and the Cauchy Integral Formula.

## Homework Equations

Evaluate the complex integral: ∫e^(e^it) dt, from 0 to 2∏

## The Attempt at a Solution

I cannot find an appropriate substitution for the integral.

Perhaps the best way to see how to do this question is that we somehow need to make this into a contour integral. The easiest things around which to integrate are circles right? For example, if f(z) is a complex function and we want to integrate around the unit circle $\{ z \in \mathbb C: |z|^2 = 1 \}$, it may be convenient to parameterize the circe as $z = e^{it}$. Thus if somebody asks you to integrate $e^{e^{it}}$ for $t \in [0,2\pi)$, what function is being integrated about what contour?