Enhancing CAS improper integrals computations using extensions of the residue theorem

Abstract

In a previous paper, the authors developed new rules for computing improper integrals which allow computer algebra systems (CAS) to deal with a wider range of improper integrals. The theory used in order to develop such rules where Laplace and Fourier transforms and the residue theorem. In this paper, we describe new rules for computing symbolic improper integrals using extensions of the residue theorem and analyze how some of the most important CAS could improve their improper integral computations using these rules. To achieve this goal, different tests are developed. The CAS considered have been evaluated using these tests. The obtained results show that all CAS involved, considering the new developed rules, could improve their capabilities for computing improper integrals. The results of the evaluations of the CAS are described providing a sorted list of the CAS depending on their scores.