If you want to convince somebody that a particular natural number is prime, you can hand them a primality certificate--a small bundle of data which can be used to efficiently generate a proof of primality. Does anything similar exist for elementary functions with no elementary antiderivative? Do theorems exist in differential Galois theory (or other fields) which allow us to construct "non-integrability certificates" for, say, $e^{x^2}$ or $\log(\sin x)$?
2026-04-13 21:03:36.1776114216
Can an integral be certifiably non-elementary?
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