Calculation of the volume potential for ellipsoidal bodies

We consider quadrature formulas for calculating the integral of the product of functions, one of which has an integrable singularity admitting exact calculation of the integral. Basing on these formulas, we suggest a method for calculating numerically the potential of the ellipsoid without cutting out a region near the singularity. We approximate the inner integral by a function with a weak logarithmic singularity, and a subsequent change of variables enables us to perform further numerical integration without singularities in the integrand. For simulations we construct a quite complicated test function amounting to the exact potential of an ellipsoid of revolution with an elliptic density distribuion.