Rule-based integration: An extensive system of symbolic integration rules

Abstract

Finding the antiderivative of expressions is often challenging and requires advanced mathematical skills even for simple looking problems. Computer algebra systems (CAS) like Mathematica (Wolfram Research, Inc., Champaign, IL), Maple (Maplesoft, a division of Waterloo Maple Inc., Waterloo, Ontario), and Maxima (maxima.sourceforge.net) provide integrators to compute antiderivatives symbolically. However, these systems give no insight as to how an antiderivative is found or why it could not be computed. Also, they use advanced methods incomprehensible to humans that often result in huge antiderivatives unnecessarily involving special functions.