I have a function $f(x,y,z)$ such that
is finite, and I want to approximate this integral.
I'm familiar with quadrature rules and monte carlo approximations of integrals, but I see some difficulties implementing them with in an infinite domain. In the monte carlo case, how does one go about sampling an infinite region (especially if the regions that contribute more significantly to the integral are unknown)? In the quadrature case, how do I find the optimal points? Should I simply fix an arbitrarily large region centered around the origin and apply sparse quadrature rules? How can I go about approximating this integral?