$$\mbox{Integrate } \int_{|z|<1} \frac{1}{z^k\cos z}dz \mbox{ where } k \in \mathbb{Z}^+, z \in \mathbb{C}.$$
We have $\frac{1}{\cos z}$ is analytic in $|z| < 1$ and $|z|< 1$ is closed, let $z_{0}=0 $ then by Cauchy’s Integral Formula and Cauchy’s Integral Formula for Derivatives we have the result. Am I right?
Could you help me, if it is right?