Consider a function $P$ which integrates to unity in full space. $$ P(a,b,c,d) = \exp\left[a^2 + b^2 + c^2 + d^2\right](a-b)(b-c)(c-d) $$ I need to eliminate $d$.
One way is to perform a linear transformation in which variables $a,b,c$ can be expressed in terms of $d$ and finally it can be integrated out. This is just a vague idea. I am really not sure if this will work and even if it does, I don't know how to proceed.
Also I would like to know if there is any other way to do this exercise.