Hi.
In the axiom manual I find
"Integration is the reverse process of differentiation, that is, an
integral of a function f with respect to a variable x is any function g
such that D(g, x) is equal to f.
....
Given an elementary function to integrate, Axiom returns a formal
integral as above only when it can prove that the integral is not
elementary and not when it cannot determine the integral. In this rare
case it prints a message that it cannot determine if an elementary
integral exists.
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
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?
Thank you
Stefano
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