[Axiom-mail] Non elementary integration

[Stefano Simonucci]

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