# Numerical evaluation of a triple integral

let be the integral

$$\int_{0}^{\infty}dx\int_{0}^{\infty}dy\int_{0}^{\infty}dz \frac{f(x,y,z)}{(1+x^{2}+y^{2}+z^{2})^{s}}$$

here $s$ is a parameter so the integral converges

now let us make the change to polar coordinates , however the function $f(x,y,z)$ will not be invariant under rotations so there will be an extra integration over the angular variables

$$\int_{\Omega} d \Omega \int_{0}^{\infty}r^{2}f(r, \Omega )(1+r^{2})^{-s}$$

my question is can we ALWAYS integrate with Numerical (MOnte carlo method) inside the angular variables $\int_{\Omega}d \Omega$ so we are left only with a sum of one dimensional integrals ??

$$\sum_{i} \int_{0}^{\infty}dr f(r, \Omega _{i})r^{2}(1+r^{2})^{-s}.$$

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