I'm supposed to show that$$\
\sqrt{\frac{2}{π}}\int\_{0}^{\infty}x^{r-1} e^{\frac{-(\log x)^2}{2}}dx=e^{\frac{r^2}{2}}$$ then $r\in \mathbb{N}$ 

I tried substituting $\log x = y$ without any success and I'm pretty stuck at the moment. Some help would be appreciated.