Is the function $\displaystyle \frac{1}{|x+y|}$ a joint probability density function? That is, is $\displaystyle \int\hspace{-6pt}\int_{\mathbb{R}^2} \frac{1}{|x+y|} \ dA$ equal to 1 and is $\displaystyle \frac{1}{|x+y|}$ nonnegative?

This problem is really giving me a headache, been attempting it for a week now and the deadline's today.