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

In terms of pen to paper calculus, integration is just as straighforward and “rule based” as integration is, albeit a bit more involved. Programming a calculator to do it is exactly the same but in “reverse” with more steps