I am stuck calculating the integral $\int_{\gamma_1} \frac{dz}{z(z-i)}$ over $\gamma_1 = Re^{it}, R>1$.
If I had to integrate over $\gamma_2 = re^{it}, r < 1$, I could just expand the integrand into a power series (using the geometric series) around $z=0$, but with $R>1$ this approach won't work. I quite frankly don't have any other idea on how to approach this.
Any hints?