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ELI5: How do integral calculators work? (lemmit.online)

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The original was posted on /r/explainlikeimfive by /u/MindfulWonderer_ on 2023-10-03 01:01:15.

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?

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