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It is mentioned in a different thread that $U(x)=\sin\left(\dfrac1{\ln(1+x^2)}\right)$ is an elementary function. My question is, how do you integrate it then?

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The thing is that $$\int_0^t \sin\left(\frac{1}{\log(1+x^2)}\right)dx$$ is not elementary. Similarly, $\dfrac{\sin x}x$ is elementary, while its integral is not. –  Pedro Tamaroff Mar 1 '13 at 21:28
According to Liouville's theorem, the antiderivatives of certain elementary functions cannot themselves be expressed as elementary functions: en.wikipedia.org/wiki/… –  Chris Mar 1 '13 at 21:29
I don't think it can be expressed through elementary functions. WA couldn't find it, so chances that it is so indeed are high. –  Kaster Mar 1 '13 at 21:30
It might be a good idea to link to the "different thread". –  joriki Mar 1 '13 at 21:37

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