Let $f(\alpha, \beta) = \int_0^{\infty} dx \: \frac{x^{\alpha}}{1+2 x \cos{(\pi \beta)} + x^2}$,  
 defined inside the unit square.  
Then we have $f(\alpha, \beta)=f(\beta, \alpha)$

But why? A mystery so deep it will never be uncovered. Its not provable. We are looking into the symmetric eyes of God.

Reference : http://math.stackexchange.com/questions/268789/symmetry-of-function-defined-by-integral