I'm trying to determine if the following double integral is convergent in the first quadrant $$ \iint \frac{1}{1+x^3+y^3} dx dy$$
I tried polar coordinates and got $$ \int_{0}^{\infty} \int_{0}^{\pi/2} \frac{r}{{1+r^3(\cos^3 \theta + \sin^3 \theta)}}\, dr d \theta$$
But it does not get any easier! Any tips to solve this type of questions?