1. The problem statement, all variables and given/known data Discuss the convergence of the integral 1/[x^2 + y^2 + z^2 + 1]^2 dxdydz in the whole space. 2. Relevant equations 3. The attempt at a solution Since the space is unbounded, the integral is an improper integral so we can consider a sphere with radius N and take the limit as N goes to infinity. I have used spherical coordinates. Theta is between 0 and 2Pi, Phi is between 0 and Pi, and rho is between 0 and N and the integrand becomes (rho^2)sin(Phi)/[1 + (rho^2)] d(rho) d(phi) d(theta) . Here again we use substitution : rho = tan x and the integrand becomes ((sin x)^2)d(x). But i can't figure out how to go on then? Is this integral convergent?