Calculating Integrals with Cauchy Formula

[player1_1_1]

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?

 

[snipez90]

Yes, and yes for the other one where C is an ellipse.