Numerical integration of the interaction energy of two point charges

We calculated numerically the energy interaction of two point charged particles. The integral has simple analytical result but is not easily solved numerically. Commercial programs as Mathematica 3.0™ and Maple V™ could not evaluate the integral and Gauss–Legendre method gave poor results. The method of Runge–Kutta integration was capable of solving it with good results. This integral showed to be a useful prototype for definite integration for double integration with poles.