I am not interested in algorithms per se, but in real use of the program. 
There exist special functions which are defined in terms of integrals (for 
instance erf), and which can be manipulated (differentiated, taylor series, 
numerical evaluation...) as if they were "elementary". In the real world, 
these are needed. My question, rephrased in order to avoid detours is, how 
difficult is it to incorporate new integrals into Axiom's inners, let it be 
knowledge base, decision table or whatever?

BTW, it does not seem true that Axiom is based solely on a decision process. 
>From the manual it mentions explicitly the use of tables of integrals and it 
already provides functions such as erf() and the like, so definitely some 
work has been done that goes beyond elementary functions.

Juanjo

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