# Integral with cauchy formula

## Homework Statement

using cauchy integral formula calculate
$$\int\limits_C\frac{e^{2z}}{z^2-4}\mbox{d}z$$
where $$C$$ is closed curve (point $$z=2$$ is inside)

## The Attempt at a Solution

$$\ldots=\int\limits_C\frac{e^{2z}}{(z-2)(z+2)}\mbox{d}z=\int\limits_C\frac{f(z)}{z-2}\mbox{d}z=2\pi if(2)=2\pi i\frac{e^{2\cdot2}}{4}=\frac12\pi e^4i$$
is it correct?