> Unfortunately, I know little about symbolic
> integration techniques. Does anybody have suggestions for references?
there are basically two techniques for symbolic integration:
1) table lookup in some classes of integrals. Maple is quite good at this.
2) recognition of some inputs that (may) admit an integral in a given class,
and computation of that integral by an algorithm. Axiom is quite good at
this.
For 2), a good reference for the transcendental case is the following book:
@Book{Bronstein97,
author = "Manuel Bronstein",
title = "Symbolic Integration {I}. Transcendental Functions",
publisher = "Springer",
year = 1997,
volume = 1,
series = "Algorithms and Computation in Mathematics"
}
Unfortunately Manuel Bronstein died before finishing vol. II on the algebraic
case, which is the difficult one. As far as I know, he did implement his
algorithms in Axiom, including (partly) the algebraic case.
Implementing symbolic integration from scratch is a major task, that would
require years before reaching what Axiom can do. In any case, I suggest
reusing the Axiom test suite as starting point.
Paul Zimmermann
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