Please help me with this Integral Calculate the integral (complex):

$$\oint_{D(0,1)}\overline ze^z \mathrm dz$$

While $D(0,1)$ is the unit circle.

Collecting the hints from the comments in an answer:
On the unit circle, we have $\overline{z} = \dfrac{1}{z}$. Hence the integral can also be written
$$\int_{\lvert z\rvert = 1} \frac{e^z}{z}\,dz,$$
which by the Cauchy integral formula evaluates to
$$2\pi i e^{0} = 2\pi i.$$
