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This question already has an answer here:

If the integral of a derivative of a function produces the original function (within a constant), why are integrals referred to as anti derivatives rather than inverse derivatives?

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marked as duplicate by Parcly Taxel, Claude Leibovici calculus Mar 4 '18 at 8:33

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Inverse functions are unique, whereas antiderivates are actually infinite (one for every choice of the integration constant.)

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Well, "anti-" means the same as "inverse" (i.e., opposite to), so I guess it is just a matter of choice and tradition. For me, at least, the word "antiderivative" sounds better, but maybe it's just what I'm used to.

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