I have myself implemented symbolic integration in Giac/Xcas in a spirit similar to Maxima or Axiom that is a few dozens *algorithms* for some classes of integrands, then the Risch algorithm in the rational case, like Maxima while it seems that Axiom implements the more general algebraic Risch algorithm. It is completely different from these thousands *rules* (if chapter 1.2.1 is representative of all the rules) : I mean that in an algorithm you compute, and that reduces the number of cases drastically. I'm really not convinced that it is worth adding these kind of rules to Giac/Xcas, but of course I don't speak for other CAS authors.
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