Integrate $e^{f(x)}$ Just wondering how I can integrate $\displaystyle xe^{ \large {-x^2/(2\sigma^2)}}$
Tried using substitution where $U(x) = x^2$ but I kept getting a $x^2$ at the denominator which is incorrect.
I understand that $\displaystyle \int e^{f(x)} = e^{\large \frac{f(x)}{f'(x)}}$ if $f(x)$ is linear, however, how do we handle this situation when $f(x)$ is not linear?
Step by step answer will be awesome!!!! thanks :D
M

$$\int{xe^{\frac{-x^2}{2\sigma^2}}dx}$$
Let $u=x^2$.  Then $\frac{du}{2}=xdx$.
$$\frac{1}{2}\int{e^\frac{-u}{2\sigma^2}}dx=-\sigma^2e^{\frac{-x^2}{2\sigma^2}}$$
