Evaluate $$\int_{\gamma}\frac{1}{z^2+2}dz$$ where $ \gamma(t) = 2i + e^{it} $ and $ 0\leq t \leq 2\pi$
I have already solve a question that was a minus signal instead of a plus signal, and in that question I have used the Cauchy's integral, but for this question, I have some problems to do the $\frac{f(z)}{z-a}$ part of the solution.