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Again, I'd like to say, AXIOM is the most powerful Computer Algebra System. Its powerful, rich, strong and dynamic type system allows using type deduction to "prove" (Curry–Howard correspondence). For example, by its implementation of Risch algorithm, it can prove integrate(sin(cos(x)),x) has no elementary expression. And it can deal with almost any indefinite integral. try this on other CAS: integrate(1/(x^3(a+bx)^(1/3)),x) (there is a lot more...)

Wow, as a emacs user, I think the "conkeror" browser is better : it's entirely based on firefox, but uses javascript as its extension languge. Just like Emacs, kernel + extension , instead of lightweight or 'unix philosophy'

Well, there is a expression that mathematica can not Integrate[] it, but AXIOM can.

integrate((x/sqrt(x * x * x * x + 10 * x * x - 96 * x - 71)),x)

AXIOM is written in lisp and latex (literate programming), it's more powerful than MAXIMA.