Changes http://wiki.axiom-developer.org/290AxiomFailedToIntegrateElementaryFunction/diff -- If I try: \begin{axiom} integrate(simplify(((x^4*log(2*x)^2+(3*x^2-2*x)*exp(x)*log(2*x)+exp(2*x)-x*exp(x))/(x^4*log(2*x)^2+2*x^2*exp(x)*log(2*x)+exp(2*x))-1)*exp(2)), x) \end{axiom} I see that Axiom failed to recognize that e^4 - (e^2)^2 is zero. AFAICS similar problem appears in original example: when I trace rischNormalize I see that both e^2 and e^4 appear in "normalized" function. But this may cause trouble later, since Axiom assumes that different kernels are algebraically independent. I do not know if rischNormalize is supposed to simplify constants (maybe this shoud be done by a separtate pass) but failing to recognize "transcendental" zero may give wrong results and otherwise Risch algorithm may declare an integrable function as non integrable.
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