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calculus - How can you prove that a function has no closed form integral? - Mathematics Stack Exchan

It is a theorem of Liouville, reproven later with purely algebraic methods, that for rational functions $f$ and $g$, $g$ nonconstant, the antiderivative $$\int [f(x)\exp(g(x))] \, \mathrm dx$$ can be expressed in terms of elementary functi...

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