Probability density function integral not converging

[ArcanaNoir]

Homework Statement

Let $f(x,y)=xe^{-xy}$ $x \geq 0, y \geq 1$
is this a probability density function? If not, find a constant that makes it a pdf.

Homework Equations

To be a pdf, we must have $\int_1^\infty \int_0^\infty \! xe^{-xy} \, \mathrm{d} x \mathrm{d} y=1$

The Attempt at a Solution

My problem is, I find the integral to be not convergent. So does my calculator. Do I have the bounds wrong? What's wrong here?

And don't mind the infinity in the integral, I know you're supposed to put the limit as some dummy variable goes to infinity.

 

[ArcanaNoir]

Never mind, I reversed the order of integration and everything was fine. It didnt occur to me you could do that, new material.