Abstract
The present paper deals with some specially devised methods that enable the numerical integration of functions with second-degree denominator roots. The main feature of these methods is that the polynomial interpolation is carried out for the non-singular numerator rather than for the whole integrand function. Therefore, the errors due to interpolation close to the singular point are avoided. The numerical quadrature formulas presented yield finite part approximations for intervals encompassing the singular point and thus are practical equivalents of the indefinite integral. The remainder terms are derived and it is shown that the improvement in terms of computing time is significant as compared to usual integration methods.
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