 Cylindrical volume element

For $x=r\cos \varphi$, $y=r\sin \varphi$ and unchanged $z$, the Jacobian determinant of Cartesian coordinates with respect to cylindrical coordinates is $r$. Hence a volume integral acquires the displayed factor for $r\ge 0$. The inverse determinant is $1/r$ where $r>0$; the axis is a coordinate degeneracy.