Let $\rho^2 = x^2+y^2+z^2$ and triple-integrate the density function over the domain$\rho \in [0,1]; \theta \in [0,2\pi]; \phi \in [0,\pi]$ So you should end up with something like$\int\limits_{0}^{2\pi}\int\limits_{0}^{\pi}\int\limits_{0}^{1}\frac{ 1 }{ 1+\rho^2 }d \rho d \phi d \theta$