A possible new integral rule Is there a non-constant continuous elementary

Roland Waters

Roland Waters

Answered question

2022-06-14

A possible new integral rule
Is there a non-constant continuous elementary function f defined everywhere on the reals, where f has elementary antiderivatives, such that for every elementary g with elementary antiderivatives, the product of f and g also has elementary antiderivatives?

Answer & Explanation

Donavan Scott

Donavan Scott

Beginner2022-06-15Added 22 answers

Explanation:
in the general case i'm afraid not, but if g is can be integrated twice over R then you can use integration by parts to prove that such a function exists:
f : R R , a R { 0 }
f ( x ) = a x

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