How do you integrate
$$\frac{x}{\sigma^2} \exp \left( \frac{-x^2}{2\sigma^2}\right)$$
I have so far tried integration by parts and have gotten stuck.
$$u= \frac{x}{\sigma^2}$$
$$du= \frac{1}{\sigma^2}$$
$$v= \frac{ -\sigma^2 \exp \left ( \frac{-x^2}{2\sigma^2} \right ) }{x} $$
$$dv= \exp \left( \frac{-x^2}{2\sigma^2} \right)$$
Then I am completely stuck
As told André Nicolas sigma is just a constant, and if you let $ω=\frac{-x^2}{2σ^2}$ we'll have:
$$\int \:\frac{\:x\cdot \:e^{^{\frac{-x^2}{2σ^2}}}}{σ^2}dx=-\int \:\:e^ωdω=-e^{^{\frac{-x^2}{2σ^2}}}+C$$
Where you don't understand ask me.