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Homework Statement:

Evaluate integral
$$I=\int_{0}^{\infty} \int_{0}^{\infty} \frac {x^2+y^2}{1+(x^2y^2)^2} e^{2xy} dx dy$$
Relevant Equations:
 ##J=\frac {\partial {(x,y)}}{\partial {(u,v)}}##
From the equations, I can find Jacobians:
$$J = \frac {1}{4(x^2 + y^2)} $$
But, I confuse with the limit of integration. How can I change it to u,v variables? Thanks...
$$J = \frac {1}{4(x^2 + y^2)} $$
But, I confuse with the limit of integration. How can I change it to u,v variables? Thanks...