I am not sure if this question has been asked here before, but if it has, I’ll delete this one.
Is there an algorithm or theorem that can be used to verify if the integration of a function is expressible with elementary functions?
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6See Luoville’s Theorem and Risch Algorithm – kiyomi Feb 05 '18 at 08:42
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You can also look at some of the Related questions on this page. – Gerry Myerson Feb 05 '18 at 08:53
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2Related: https://math.stackexchange.com/questions/155/how-can-you-prove-that-a-function-has-no-closed-form-integral – Hans Lundmark Feb 05 '18 at 10:08