Argument Principle Application

Question

$f(z)=z^3e^z$ and $\Gamma$ be the circle $z=e^{i\theta}$ where $d\theta$ varies from $0$ to $4\pi$. Then find

$$\int_{\Gamma} \dfrac{f’(z)}{f(z)}dz.$$

I applied the argument principle and got the answer as $2\pi i\cdot(3-0)$

Answer 1

No, not quite. Notice that $\Gamma$ winds twice around the origin.