find this integral with complex number

Question

$$\int \frac{(z^{-3})e^{1/z}}1dz$$

I use tailor series but I cant solve it also I use common solution but I cant solve it

Answer 1

$\int z^{-3}e^{1/z}dz=- \int u(z)v'(z) dz$, where $u(z)=1/z$ and $v(z)=e^{1/z}$.

Your turn !

Answer 2

The Solution is

$$ \int z^{-3}\, e^{1/z} dz=\frac{e^{\frac{1}{z}} (z-1)}{z}. $$