Solution
= Solution
Use <spherical polar coordinates> with $\theta$ measured from the positive $z$ axis and $\phi$ around that axis:
$$
\boxed{x=r\sin\theta\cos\phi,\quad y=r\sin\theta\sin\phi,\quad z=r\cos\theta,\qquad dV=r^2\sin\theta\,dr\,d\theta\,d\phi.}
$$
The standard full-space ranges are $r\geq0$, $0\leq\theta\leq\pi$, $0\leq\phi<2\pi$. The factor $r^2\sin\theta$ is the absolute <Jacobian determinant> and gives the <volume element>.