Why this integral diverge? For $D=[0,+\infty)×[0,+\infty)$ and $f(x,y)=(1+x+y)^{-1}$, why does the integral over $D$ of $f(x,y)$ not converge? 
It's not like $\rho/(1+\rho|\sin\theta+\cos\theta|)$ which to infinite is like $1/(|\sin\theta+\cos\theta|)$ and, close to $0$ is like $0$?

Intuitively, the area of the domain grows like $xy$, while the integrand decreases like $\dfrac1{1+x+y}$, which is insufficient to compensate.
