Normally Ordered Expansion of the Even-Power of the Radial Coordinate Operator

By virtue of the technique of integration within an ordered product of operators we derive the concise normally ordered expansion of even-power of radial coordinate operator via the equation r = ∫d³x|x > < x|r, where |x > is the three-dimensional coordinate eigenvector, and r = (x² + y² + z²)^1/2. The applications to perturbation theory is briefly discussed.