I have to find $\alpha, \beta \in \Bbb R$ for which $$ \int\_{\Bbb R^2} \frac{dx}{|x|\_{\infty}^\alpha(1+|x|\_{\infty}^\beta)} < \infty$$ using Fubini's theorem. Note that $x = (x\_{1},x\_{2})$ and $|x|\_{\infty}=\max(|x\_{1}|, |x\_{2}|)$ . 

Any help/tip would be greatly appreciated!