FYI, there is also an Emacs extension axiom-environment [1], which is 
very nice and it has Org-mode support: ob-axiom.

The Risch algorithm implemented in FriCAS is still incomplete, there are a 
few holes
in the mixed algebraic-transcendental case.

There is a right parenthesis missing in "(12) -> sum(1/k,k=1..100", page 4.
And a typo "dispkay => display" on page 4.

There is a right parenthesis missing in "(16) -> exp(%pi*sqrt(163.0)", page 
5;
"(24) -> expand((x+2*y-3*z)^5", page 6;
"(36) -> solve[x^2-y^2=4,x*y=3],1.0e-10)", left parenthesis, page 7;
"(39) -> limit(x/sqrtx^2-1,x=%plusInfinity)", parenthesis missing, page 7;
"(106) -> expand((x-2*y+3*z)^3", page 20;
"”Axiom: The Scientific Computation System”", quotes don't match, page 23;
"”diff ”", quotes don't match, page 24;
"”difference”", quotes don't match, page 25.

Typo "ploat => plot" on page 14.

Generally speaking, this is a good introduction.

[1] https://bitbucket.org/pdo/axiom-environment

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