This is a general introduction. Hi.

I came up with this today I thought it was sort of ok...

$\displaystyle \int_{-\infty}^\infty\frac{dx}{(1+x^2)^n} \approx \sqrt{\frac{2\pi}{2n-1}}$

It's better for larger values of $\displaystyle n$ but it works for smallish ones too. In the case $\displaystyle n = 1$, the $\displaystyle LHS = \pi$ and $\displaystyle RHS = \sqrt{2\pi}$, which is sort of close, right? :)