I need to solve the following complex integral
$$ \oint_{\gamma}z^4\sin(z)dz $$ where $\gamma:=\{z\in\mathbb{C}:|z-2|=2\}$.
But I see that $f(z)=z^4\sin(z)$ is holomorphic in $\gamma$ so, by Cauchy's integral theorem this integral must be zero.
I feel that I have a mistake, If I have it, can someone tell me which is it?