Compute $$\int_{|z|=1}\frac{e^z}{z^n}dz$$
Im thinking of using cauchy's integral formula since it satisfies the properties.
So we just have $$\int_{|z|=1}\frac{e^z}{z^n}dz=\frac{2i\pi}{(n-1)!}e^0=\frac{2i\pi}{(n-1)!}$$
This is the first time i'm doing this so i'm not sure if i did it right.
I would personally have gone with the Residue theorem, because I find that easier. Assuming $n \geq 1$, the residue (i.e. the coefficient of $\frac1z$ in the Laurent series) of $\frac{e^z}{z^n}$ at the single pole $z = 0$ is $\frac{1}{(n-1)!}$. Thus the integral in a counterclockwise direction around that pole is equal to $2\pi i\frac1{(n-1)!}$.