How can I use Cauchy integral formula to calculate the following integral
$\int_{\partial \mathbb{D}} \dfrac{f(z)}{z^n}dz$
where $f $ is entire, $\mathbb{D}$ denotes the unit disc, and $n \geq 1$ is a real constant.
Can I use the Cauchy integral Formula - Higher derivatives version with $\Gamma(n)$ instead of $n!$ ?