Calculate $\int_\gamma \frac{1}{z^2+2z+2}dz$
where $\gamma$ is the circle with centre 0 and radius 1.
I got the singularities of this as $(-1+i)$ and $(-1-i)$. And as the modulus of these is $\sqrt2$ they fall outside $\gamma$ so by Cauchy's Theorem this integral is 0. Does that look correct?