This is a general introduction. Hi.

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

\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?