>
> * Symbolics in general. Symbolic integration and summation. Rewriting 
> expressions. Simplifying inequalities. Simplifying expressions subject to 
> assumptions involving inequalities. Limits and generalized series 
> expansions involving special functions. Sage can do a bit of these things 
> via Maxima and SymPy, but it's nowhere near as powerful as Mathematica.
>

What concerns indefinite symbolic integration, you can use the FriCAS 
interface.  This outperforms Mathematica, Maple, Maxima and is continuously 
improved on by Waldek Hebisch.

Martin

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