How to solve this triple integral? I am wondering how I could solve the integral 
$$\iiint \frac{1-e^{-(x^2+y^2+z^2)}}{[x^2+y^2+z^2]^{2}}$$
over $\mathbb{R}^{3}$
I thought maybe I could break it up into three single integrals and multiply or something. I think it is not supposed to be difficult to solve. How should it be approached?
Thank you

Hint: Use spherical coordinates, and note that each copy of $\mathbb{R} = \left(-\infty,\infty\right)\Rightarrow I = \displaystyle \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \dfrac{1-e^{-\left(x^2+y^2+z^2\right)}}{(x^2+y^2+z^2)^2}dxdydz= 8\displaystyle \lim_{r \to \infty} \int_{0}^r \int_{0}^r \int_{0}^r \dfrac{1-e^{-\left(x^2+y^2+z^2\right)}}{(x^2+y^2+z^2)^2}dxdydz$. Can you take it from here ?
