Hi

I have the standard integral

$\displaystyle {\displaystyle \int}_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$

But need to find what

$\displaystyle {\displaystyle \int}_{-\infty}^{\infty} e^{-\alpha x^2} dx $ is using the expression above

I have found on the internet that it is $\displaystyle \sqrt{\frac{\pi}{\alpha}}$ but can't see how to get it.

I am assuming the use of changing the variable but can't see how to go about it.

Thanks, James