Complex Integral over contour C

Question

I am having difficulty evaluating the complex integral

$$\int_C \frac{dz}{(z-1)^2(z-i)} $$

over the contour $C: |z-1| = 1$.

The singularities are $z_0 = 1$ and $z_1=i$, with $z_0$ lying in the contour, so Cauchy Goursat theorem does not apply correct? Is there a way to apply Cauchy Integral Formula to this?(maybe by splitting it?)

Answer 1

Hint :

$z_1=i$ is NOT a singular point in the given region.

Take , $f(z)=\frac{1}{z-i}$. Then use Cauchy's integral formula.