Suppose I have a function $$f(x,y,z) \propto x^2yz(1-2x-y-z)$$ where $x>0,y>0, z>0, 2x+y+z<1$
I need to find the marginal functions of X, Y and Z. In normal, two-variable situations, I simply have to integrate out $Y$ across the domain of $Y$ to find the marginal distribution of $X$.
In this case, to find the marginal of $X$, I assume the standard way is: $$f(x)=\int^{1-2x-z}_{0} \int^{1-2x-y}_{0} x^2yz(1-2x-y-z) dz dy$$ which can seem a little complicated if I do it via the brute force manner. Is there a more efficient way to do this, especially considering existing distributions?
Thank you!