I want to evaluate $$\int{ \frac{\sin(\pi z^2)+\cos(\pi z^2)}{\{(z-1)(z-2)\}^{4}} dz }.$$
This is the contour integration I came across. I know Cauchy's integral formula and Cauchy's integral formula for higher derivatives. First I separate $\cos$ and $\sin$ terms. Then I cosider $f(z)= \frac{\sin(\pi z^2)}{(z-1)^4}$ and z.$=-2$ and then I use Cauchy's formula somehow. Am I right in my approach? If not, how do I proceed?