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
I believe a good chunk of how Mathematica, for example, works is based on [Meijer functions](https://en.m.wikipedia.org/wiki/Meijer_G-function).
The idea being that they can represent a very large set of “normal functions” and are trivial to integrate themselves.
So the main computational task is not the integration, per se, but the “encoding” and “decoding” of the input and result in a form that can be integrated with simple rules, and then is tolerable for humans, respectively.
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