How to evaluate contour integral I have a homework problem to evaluate the integral
$$
\oint_{\gamma}\frac{\cos z}{(z+i)^3}dz
$$
along the curve $\gamma(t)=-i+e^{it}, t\in[0,2\pi]$. I proceeded to plug the given information into the definition of a contour integral and got to the expression
$$
\oint_{\gamma}=i\int_{0}^{2\pi}\cos(-i+e^{it})e^{-2it}dt
$$
which seems hardly helpful. I don't know how to evaluate this or manipulate it any further and I suppose there is some trick earlier on to make the integration more manageable. I just can't figure it out so I'd be grateful for any help.

Hint: As Jose hints in the comments, we want to use the fact that
$$f^{(k)}(z_0)=\frac{k!}{2\pi i}\oint_{\partial B_r(z_0)}\frac{f(z)}{(z-z_0)^{k+1}}dz$$
with the correct holomorphic function $f(z)$
