Integrating a Function All Over Space in Cartesian Coordinates

Question

So as we know, if we want to integrate a function such as $\frac{1}{(x^2+y^2+z^2+4)^{3/2}}$ all over space, the easiest way is to use a change if coordinates. However, I am wondering of a way to solve it without any change in coordinates or substitution i.e. solve it as $\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f(x,y,z)dxdydz$ without any coordinate change or substitution where $f(x,y,z)$ is a function such as the one above.