Loop integrals occur in higher order perturbation calculations for the cross section of particle interactions in high energy physics. In previous work we introduced a numerical extrapolation method to handle a class of Feynman loop diagrams where the integrand shows a singular behavior on a hypersurface which may intersect the domain of integration. The integral is considered in the limit as a parameter in the integrand tends to zero. Under certain conditions, the extrapolation process achieves convergence acceleration to the limit. In order to handle massless cases, we apply a dimensional regularization technique to extract infrared divergences from the integral. We illustrate the combined technique using a scalar one-loop sample integral.