Integral $\int y\,e^{x^2}\,dy$

Question

$$\int y\,e^{x^2}\,dy$$

I begin with

$$\int e^{x^2}y\, dy$$

let $u=e^x$, $du=e^x\, dx$

how do I continue?

Answer 1

Your integral depend of $y$ only, then you can put $e^{x^2}$ out of your integral.

$$\int ye^{x^2}\mathrm{d}y=e^{x^2}\int y\mathrm{d}y=e^{x^2}\left(\frac{y^2}{2}+C\right)$$ where $C$ is a constant.