Rubi: Symbolic integrator based on an extensive system of integration rules

I encourage those interested in Computer Algebra Systems to read this comparison report: <a href="https:&#x2F;&#x2F;www.12000.org&#x2F;my_notes&#x2F;CAS_integration_tests&#x2F;reports&#x2F;summer_2022&#x2F;indexchapter1.htm#x2-10001" rel="nofollow">https:&#x2F;&#x2F;www.12000.org&#x2F;my_notes&#x2F;CAS_integration_tests&#x2F;reports...</a><p>AFAIK, this is the only recent benchmark-type study that compares modern CAS software (Mathematica vs Maxima vs FriCAS vs etc).

I used this a while back to do an awkward integral that no other CAS was able to do and was able to show up a paper that had claimed there was no closed-form solution.<p>Unfortunately the answer was in terms of hypergeometric functions and was scarcely more useful than the unevaluated integral. In any case I found Rubi to be very impressivein terms of results.<p>Digging into the code wasn&#x27;t much fun, as it&#x27;s just a colossal Mathematica rules engine, like reading Gradshteyn and Ryzhik, but with square brakets everywhere.

What is it fundamentally about symbolic integration that makes it so much more difficult to do? I mean, I studied calculus and learned any number of the rules but it&#x27;s a curious thing that one operation, differentiation is trivial, yet the opposite, integration is massively complex.

Rubi is great. When I&#x27;m stuck on an integral in Mathematica with the builtin Integrate, I load up Rubi and sometimes it can find a solution.

There is a Golang based CAS that follows the Mathematica language which makes use of Rubi for integration.<p><a href="https:&#x2F;&#x2F;github.com&#x2F;corywalker&#x2F;expreduce">https:&#x2F;&#x2F;github.com&#x2F;corywalker&#x2F;expreduce</a>

This is cool! The page by Abbasi they link to also contains a comparison between MMA and Maple in solving differential equations<p><a href="https:&#x2F;&#x2F;12000.org&#x2F;my_notes&#x2F;kamek&#x2F;kamke_differential_equations.htm" rel="nofollow">https:&#x2F;&#x2F;12000.org&#x2F;my_notes&#x2F;kamek&#x2F;kamke_differential_equation...</a>

Has anyone looked at writing a script to transform those rules for yacas? Making yacas 94% as good as Mathematica at integration sounds like a worthy goal considering how easy it is to deploy it.

Hopefully this can be integrated (no pun intended) into SymPy.