# Hi, nice approximate

$\int_{-\infty}^\infty\frac{dx}{(1+x^2)^n} \approx \sqrt{\frac{2\pi}{2n-1}}$
It's better for larger values of $n$ but it works for smallish ones too. In the case $n = 1$, the $LHS = \pi$ and $RHS = \sqrt{2\pi}$, which is sort of close, right? :)