Dear Stefano, Stefano Simonucci writes:
> Now if I write > integrate(exp(x)/x,x) > I obtain > Ei(x) > while if I write > integrate(exp(x)/x^2,x) > I get a form integral. But the integral of exp(x)/x^2 can be given in terms > of Ei(x) as exp(x). In fact I believed that the axiom can be able to find > the solution that is > integrate(exp(x)/x^2,x) --> Ei(x)-exp(x)/x this would be correct, yes. > But from the manual I deduce that exp(x)/x^2 can be prooved not elementary > integrable. Why exp(x)/x is integrable while exp(x)/x^2 not? Well, exp(x)/x is *not* elementarily integrable, Ei(x) is simply defined to be its integral. Ei(x) is *not* an elementary function. (in the mathematical sense) However, Axiom should still be able to figure out your integral. The corresponding code is in intpm.spad, but your integral doesn't fit, it seems. If you are willing to do some research, we might be able to figure out how to improve the pattern matcher. There is also code by Manuel Bronstein (written in maple), that would handle special functions. Maybe this should be integrated, too. Note that there are also two bugs (with fixes) filed on IssueTracker, so if you rely heavily on integrals, you might want to patch your axiom: http://page.axiom-developer.org/zope/mathaction/198IntegrateSinX2XIsNotHandled http://page.axiom-developer.org/zope/mathaction/199IntegrateExpX2ExpXXX The first patch is hidden in a comment, you'll have to look for it. Martin _______________________________________________ Axiom-mail mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-mail
