Breaking up a double integral product? Is this some special property? I've been tasked to solve for $a$ in the following double integral equation:
$1=\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}ae^{-(x1+x2)}dx_{1}dx_{2}$
When referencing the provided solution, my professor makes the following jump:
$1=a\int_{-\infty }^{\infty }e^{-x1}dx_{1}\int_{-\infty }^{\infty }e^{-x2}dx_{2}$
I'm curious as to why we the equation can be formatted into this form. I understand that the exponent addition can be transformed into a product, but why are you able to split up the double integral into a product?  Is this some property of double integrals?

We have $$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} ae^{-x_1+x_2}dx_1dx_2 = a\int_{-\infty}^{\infty} e^{-x_2}\underbrace{\int_{-\infty}^{\infty} e^{-x_1}dx_1}dx_2,$$ now note that the entire underbraced integral is some constant with respect to the $x_2$ integral, so it may be factored out:
$$a\underbrace{\int_{-\infty}^{\infty} ae^{-x_1}dx_1}\int_{-\infty}^{\infty} e^{-x_2}dx_2.$$
