How do integral calculators work?

Question

A derivative calculator seems a lot easier to build as it much more “rule” based and solutions are usually what you would expect them to be. But how on earth can integral calculators figure out absolutely brutal integrals like sqrt(tanx) is in less than 5 seconds?

In: 102

Answer 1

There’s no ELI5 answer but an introduction to this would be reading about the [Risch Algorithm](https://en.wikipedia.org/wiki/Risch_algorithm).