Evaluating a definite integral by changing variables. How can I evalute this integral?
$$\psi(z)=\int\limits_{-\infty}^\infty\int\limits_{-\infty}^\infty [(x-a)^2+(y-b)^2+z^2]^{-3\over 2}f(x,y)\,\,\,dxdy\;.$$
I think we can treat $z$ as a constant and take it out of the integral or something. Maybe changing variables like taking $u={1\over z}[(x-a)^2+(y-b)^2]$? But then how  do I change $f(x,y)$ which is some arbitrary function, etc?
Thanks.

There's no general way to evaluate this integral, for if there were, you could integrate any function $g(x,y)$ by calculating this integral for $f(x,y)=g(x,y)[(x-a)^2+(y-b)^2+z^2]^{\frac32}$.
