I've found many questions related to taking a "literal constant", such as 3, and pulling it outside of a double integral, but my question pertains to doing this with a variable constant. In my stats textbook, they do the following:
I see that $xye^{-(x+y)} = xe^{-x}ye^{-y}$. Is the idea that they are pulling out the $xe^{-x}$ factor into the outer integral, because it's a constant with respect to the inner integral $dy$? I'd not seen this done before in my Calc 3 class - we would have just integrated $xe^{-x}ye^{-y}$ with respect to $y$ - so I want to be sure I'm understanding it correctly.