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