ABSTRACT
This chapter explores how computer algebra systems perform symbolic integration. It examines the techniques used by computer algebra systems to integrate rational functions. The chapter describes two methods to determine the rational part of the result, one due to Charles Hermite and the other to Ellis Horowitz. It presents a technique developed independently by Michael Rothstein and Barry Trager to express the transcendental part. Since computer algebra systems typically begin the process of symbolic integration by attempting to apply heuristics, it is appropriate that we examine some of these techniques. The derivative-divides method is a variant of the method of integration by substitution taught in calculus. The method taught in introductory calculus to integrate a rational function consists of the following steps: actor the denominator into linear and irreducible quadratic factors, find the partial fraction decomposition, and integrate each partial fraction.
