Symbolic integration — the dust settles?

By the end of the 1960s it had been shown that a computer could find indefinite integrals with a competence exceeding that of typical undergraduates. This practical advance was backed up by algorithmic interpretations of a number of classical results on integration, and by some significant mathematical extensions to these same results. At that time it would have been possible to claim that all the major barriers in the way of a complete system for automated analysis had been breached. In this paper we survey the work that has grown out of the above-mentioned early results, showing where the development has been smooth and where it has spurred work in seemingly unrelated fields.

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