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Why can't $e^{x^2}$ be integrated [duplicate]

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My teacher told me that not only do we have to use the erf function to approximate error, but that it is proved impossible to integrate in real analysis (at least not Riemann-integrable). Is there a name for this proof, and can I have it? I am not a mathematician, but such a simple function has been around and it irks me terribly and need a detailed proof for closure.


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