Integrate the function (x, y) = 1/(1 + x 2 + y 2 ) 2 over the region enclosed by one loop of the lemniscate

Integrate the function ƒ(x, y) = 1/(1 + x² + y²)² over the region enclosed by one loop of the lemniscate (x2 + y²)² - (x² - y²) = 0.