Breaking up a double integral where the integrand is a simple product

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This is from the book Further Mathematics for Economic Analysis:

$\int_{-\infty}^x \int_{-\infty}^y e^{-|u|-|v|} \ dvdu$

The double integral was rewritten as:

$\int_{-\infty}^x e^{-|u|} \ du \times\int_{-\infty}^y e^{-|v|} \ dv$

I was not aware that an integrand could be split up that way; I thought it was always supposed to be solved holding one variable constant and doing one integration at a time. Is this a special property of the exponential, a special property of this specific function, or something else?