I was wondering how you proof that the function $f(x)=e^{x^2}$ does not have a primitive function. I have heard en read this example multiple times, but I don't know how to proof it.
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1Of course it has. Take $\int_0^xe^{t^2},\mathrm dt$. – José Carlos Santos May 23 '20 at 13:29
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I mean a "elementary" primitive function, so written using exponents, logs, trigonometric functions, roots, ... . So not with an integral. – flor.debois May 23 '20 at 13:32