Double integration problem

Calculus Level 5

Let \[I = \displaystyle\int \limits^{1}_{0}\displaystyle\int \limits^{1}_{0}\frac{x-1}{\left( 1-xy\right) \ln\left( xy\right) } \, dx \, dy\] Find \[\left\lfloor 1000 I\right\rfloor \]

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