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How do they stack up doing actual computer algebra things like symbolic integration?

https://www.12000.org/my_notes/CAS_integration_tests/reports...

Note that alternative open source solvers like Fricas fail 10x the integrals in that corpus.

Rubi is just rule based integration. So its like looking up a book of integral formulas and encoding them as rules. It does mean you need a minimum number of other features like partial fraction decomposition, polynomial factoring so it demonstrates some capability. Many of the other Mathematica like CAS end up using the Rubi rules themselves.

But indefinite integration is just a small aspect of CAS capabilities. What about integration over a line or surface, definite integration and dealing with singularities, differential equations, solving equations under assumptions, simplifying equations.

The same guy found Sympy was similarly far behind in differential equations (although Maple edges out Mathematica here):

https://www.12000.org/my_notes/CAS_ode_tests/index.htm

He does a few other side-by-side comparisons but doesn't include open source engines in them.

The bottom two are based on Wolfram engine itself, so would fair the same as Mathematica. I do not know about the first one.

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