This question's been killing me for hours.
My assumption is that when they ask for the density of X they're asking for the marginal density function f(x). In this case you would take the integral of f(x,y) over all values of y, or in other words, the integral of f(x,y) from 0 to infinity. However, when I do this it becomes infinity. The same goes for trying to compute the density of Y.
Could somebody show me what I'm doing wrong?