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
Your instinct is correct. You can take a derivative by following a simple procedure, and it is very easy to write a computer algebra system that can take derivatives.
Computing integrals is *not* easy, and there is no procedure that works in all cases. For both humans and computers, computing integrals requires a library of tricks and pattern matching, and speculative trial and error.
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