Symbolic Integration: The Stormy Decade Three approaches to symbolic integration in the 1960's are described. The first, from artificial intelligence, led to Slagle's SAINT and to a large degree to Moses' SIN. The second, from algebraic manipulation, led to Manove's implementation and to Horowitz' and Tobey's reexamination of the Hermite algorithm for integrating rational functions. The third, from mathematics, led to Richardson's proof of the unsolvability of the problem for a class of functions and for Risch's decision procedure for the elementary functionseneralizations of Risch's algorithm to a class of special functions and programs for solving differential equations and for finding the definite integral are also described. CACM August, 1971 Moses, J. integration, symbolic integration, definite integrals, rational functions 3.1 3.2 3.6 4.9 5.2 5.9 CA710808 JB February 2, 1978 2:48 PM 2164 4 2164 2170 4 2164 2323 4 2164 2719 4 2164 2167 5 2164 2164 5 2164 2164 5 2164 2164 5 2164 2323 5 2164 2164 6 2164 2167 6 2164 2170 6 2164