$$\iint\_{\mathbb{R}^2} \frac{1}{\sqrt{1+x^4+y^4}}$$ converges or diverges?

I've tried to change to polar coordinates but i got stuck really quick  

$$\int\_{0}^{2\pi}\int\_{0}^{\infty}\frac{r}{\sqrt{1+r^4(1-2\sin^2(t)\cos^2(t))}}drdt$$  

any hint please?