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...)