Integral of $xe^y \,dy$ I tried integration by parts but that leaves me with $xe^y$ - integral of $e^y \,dx$.

As far as I know that should leave me with $xe^y - xe^y$ which is $0$. My book says its $xe^y$.

It doesn't seem like substitution is going to work because I have two variables.

If you can explain this to me I'd appreciate it.
Of course it is $xe^y$:$$\int xe^y\,\mathrm dy=x\int e^y\,\mathrm dy=xe^y.$$In this problem, $x$ is a constant.
If $x$ does not depend on $y$,

$$\int xe^ydy=xe^y+C$$

and if it does

$$\int x(y)\,e^ydy$$

cannot be solved by lack of information on the relationship.