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
Integration, in college courses, is normally “here’s a bunch of things that *might* work, eventually you’ll learn to recognise the most promising tool for any given problem”
However, there is actually an algorithm (a step by step procedure) for integration. Unfortunately, it’s far far more complicated than the one for differentiation.
From [Wikipedia](https://en.wikipedia.org/wiki/Risch_algorithm):
>The complete description of the Risch algorithm takes over 100 pages
so it’s not the sort of thing you can expect a human to commit to memory. However, it can be coded into computer algebra software.
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