$\displaystyle f_{X,Y}(x,y)=f_X(x)*f_Y(y)$Let $\displaystyle f_{X,Y}(x,y)=C(x^2+y^2+1)^{-2}$. Set $\displaystyle C$ so that the two vector components will be independent.

I can get $\displaystyle f_X(x)$ (and similarly $\displaystyle f_Y(y)$) as $\displaystyle \int_{-\infty}^\infty f_{X,Y}(x,y)dy$, but I can't integrate it. I suspect this isn't the right way to proceed.

The solution given is: "There is no such $\displaystyle C$."