Question

what is the integral of e^x . x dx ?

Answer 1

Integrate by parts:
\[\int xe^x\;dx\]
\[\begin{matrix}u=x& & &dv=e^x \;dx\\
du=dx& & &v=e^x\end{matrix}\]
\[\int x e^x\;dx=xe^x-\int e^x\;dx\]