2164	 Symbolic Integration The Stormy Decade	 Three approaches to symbolic integration in the 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 functions.Generalizations 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. integration symbolic integration definite integrals rational functions
