The problem is : Is $f(x,y)=\frac{xy}{(1-|x|)^2+(1-|y|)^2}$ Lebesgue integrable on $[-1,1] \times [-1,1]$ ?
What is the value of $\int\int \frac{xy}{(1-|x|)^2+(1-|y|)^2} dydx $ and $\int\int \frac{xy}{(1-|x|)^2+(1-|y|)^2} dxdy $ ?
I tried to show that $\frac{|x|}{(1-|x|)^2}$ is lebesgue integrable. (Since $\frac{|xy|}{(1-|x|)^2+(1-|y|)^2} \leq \frac{|x|}{(1-|x|)^2}$)
But it was hard. Is it really lebesgue integrable?