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## Main Question or Discussion Point

I have the integral

[itex]\int_{-\infty}^{\infty}dx \int_{-\infty}^{\infty}dy e^{-\xi \vert x-y\vert}e^{-x^2}e^{-y^2}[/itex]

where [itex]\xi[/itex] is a constant. I would like to transform by some change of variables in the form

[itex]\int_{-\infty}^{\infty}dx F(x) \int_{-\infty}^{\infty}dy G(y)[/itex]

the problem is that due to absolute value in the integral one must take in account where x is greater or less than y,

can someone help me, please?

[itex]\int_{-\infty}^{\infty}dx \int_{-\infty}^{\infty}dy e^{-\xi \vert x-y\vert}e^{-x^2}e^{-y^2}[/itex]

where [itex]\xi[/itex] is a constant. I would like to transform by some change of variables in the form

[itex]\int_{-\infty}^{\infty}dx F(x) \int_{-\infty}^{\infty}dy G(y)[/itex]

the problem is that due to absolute value in the integral one must take in account where x is greater or less than y,

can someone help me, please?