# Analytic integration formula?

Has it been proven that there is no formula for analytic integration? Is this still open, could there be a formula?

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What do you mean? Do you mean an algorithm for symbolic integration? There is one that almost works: en.wikipedia.org/wiki/Risch_algorithm –  Potato Jun 15 '12 at 9:07
I am not sure what the question is. –  Eric Naslund Jun 15 '12 at 9:26
a reference: Integration in Finite Terms. Maxwell Rosenlicht. The American Mathematical Monthly, Vol. 79, No. 9 (Nov., 1972), 963-972. –  GEdgar Jun 15 '12 at 15:38
@EricNaslund: I believe that the OP is trying to find if there is a general formula or method that can be applied to a wide variety of integrals. I was wondering something similar. I started with a product of two functions of $x$, and tried to work backwords to find the integrals and sums that would create them. I thought that I may be able to find a method that could start with a wide variety of functions, and convert them between integrals and summations. This seems to hint that this is very hard... –  Matt Groff Jul 17 '12 at 22:23
I basically want to know if there is a proof that there is no such formula similar to the differentiation formula for analytic integration. –  Niklas rtz Jul 19 '12 at 5:16

In which case the answer is no, though as previously stated the Risch algorithm gets you most of the cases where they do exist. Try solving $\int \sin(x^2)$, for example (but don't try too hard).