Risch Algorithm for Symbolic Integration

I recently read about Rubi, which instead uses a huge decision tree and pattern matching to do symbolic integration. Kind of like how humans do it. There are a lot of interesting thoughts on their website, I would highly recommend checking it out. Skimming through the pdfs of rules was a lot of fun.

https://rulebasedintegration.org/

SymPy implements this algorithm, start here: https://github.com/sympy/sympy/blob/master/sympy/integrals/r...

Not all of it, notably the algebraic extensions which are quite difficult to grasp.

The Risch Algorithm was mentioned in a recent XKCD[1]. Perhaps that was the trigger for this submission.

There were a few rabbit holes to investigate from that comic. Bessel functions were what first piqued my curiosity. I never did get around to the Wikipedia page, but Wikiquote[2] had some interesting quips.

[1]: https://xkcd.com/2117/ [2]: https://en.wikiquote.org/wiki/Bessel_function