A Heuristic Program that Solves Symbolic Integration Problems in Freshman Calculus

A large high-speed general-purpose digital computer (IBM 7090) was programmed to solve elementary symbolic integration problems at approximately the level of a good college freshman. The program is called SAINT, an acronym for "Symbolic Automatic INTegrator." This paper discusses the SAINT program and its performance. SAINT performs indefinite integration. It also performs definite and multiple integration when these are trivial extensions of indefinite integration. It uses many of the methods and heuristics of students attacking the same prombles. SAINT took an average of two minutes each to solve 52 of the 54 attempted problems taken from the Massachusetts Institute of Technology freshman calculus final examinations. Based on this and other experiments with SAINT, some conclusions coneering computer solution of such problems are: (1) Pattern recognition is of fundamental importance. (2) Great benefit would have been derived from a large memory and more convenient symbol manipulating facilities. (3) The solution of a symbolic integration problem by a commercially available computer is far cheaper and faster than by man.