A hybrid integral for parametrized rational functions

Abstract

We present a hybrid integral to obtain symbolic results of an indefinite integral where the integrand is an univariate rational function whose coeficients have a parameter. We consider calculating power series roots of the denominator polynomial by applying Hensel construction. Accurate numerical results for a definite integral are easily obtained by simple substitutions of upper and lower bounds of integral into obtained approximate symbolic results.Numerical experiments show that the hybrid integral works well around the expansion point of the power series roots.