Double integral in polar coordinates problem

[Steff_Rees]

Homework Statement

\int_{y=-infinity}^{infinity} \int_{x=-infinity}^{infinity} (x^4+y^4)/(1+x^2+y^2)^4 dx dy

Homework Equations

i'm not sure what the new limits are after the transformation to polar coordinates and how to solve the integral.

The Attempt at a Solution

i have my new function of integration to be
(r^4*cos^4(theta)+r^4*sin^4(theta))/(1+r^2)^4 r dr d\theta

 

[Char. Limit]

Homework Statement

$$\int_{y=-\infty}^{\infty} \int_{x=-\infty}^{\infty} \frac{x^4+y^4}{(1+x^2+y^2)^4} dx dy$$

Homework Equations

i'm not sure what the new limits are after the transformation to polar coordinates and how to solve the integral.

The Attempt at a Solution

i have my new function of integration to be
$$\frac{r^4 cos^4(\theta)+r^4 sin^4(\theta)}{(1+r^2)^4} r dr d\theta$$

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