Integrate $||x||^{-\alpha}$ on $[a,b]\times [c,d]$

Question

Consider $\alpha >1$ and let $a,c>0$ and $a<b$, $c<d$. How can I compute $$\int_{[a,b]\times [c,d]} ||(x_1,x_2)||^{-\alpha} dx=\int_{[a,b]\times [c,d]}\frac{1}{(x_1^2+x_2^2)^{\frac{\alpha}{2}}} dx$$ For a ball with some center one may use polar coordinates but I have no idea what to choose for a rectangle $[a,b]\times [c,d]$. If this is possible I'm guessing that we may just find a "good" transformation which helps to evaluate the integral. I would be grateful for any hints how to choose such transformation!