I'm trying to compute the following integral: $$\int_{\gamma(-1;2)} \frac{dz}{(z^2+z)^2}$$ where $\gamma$ is traversed twice in a clockwise direction. I know that I can compute this integral using Cauchy's residue theorem, but my question is how do I deal with the fact that the circle is traversed twice and in a clockwise direction?
My assumption would be that I compute the integral as if it were positively oriented and only traversed once and then multiply this result by $-2$. Is this correct?