Denote by \(\lambda\) Lebesgue measure on \((-1,1)\). Show that the iterated integrals exist and coincide,

\[\int_{(-1,1)} \int_{(-1,1)} \frac{x y}{\left(x^{2}+y^{2}ight)^{2}} \lambda(d x) \lambda(d y)=\int_{(-1,1)} \int_{(-1,1)} \frac{x y}{\left(x^{2}+y^{2}ight)^{2}} \lambda(d y) \lambda(d x)\]

but that the double integral does not exist.