Complex integration of exponential function

Question

I am asked to find the integral of $z e^{z^2}$. I have applied the formula of multiplication but the factor of exp cannot be eliminated ofcourse. So how can i solve it. Sorry for such a basic question but i am badly stuck in here.

Answer 1

$$\int z e^{z^2}\mathrm{d}z \stackrel{u=z^2}{=} \frac12 \int e^u \mathrm{d}u = \frac{e^u}{2}+c=\frac{e^{z^2}}{2}+c$$

Answer 2

Introduce $u = z^2$

$\int z \mathrm{e}^{z^2} \mathrm{d} z = \frac{1}{2} \int \mathrm{e}^{u} \mathrm{d} u$.

You should be able to take it from here :)