Indefinite Integral of the Gaussian?!?!

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I state a common misconception of Calculus students; that the Gaussian has no indefinite integral, and correct it to the fact that the Gaussian has no indefinite integral in terms of elementary functions. I then show by explicit Taylor expansion that an antiderivative exists.
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the physics vibe is strong with this video

Alex-knlu
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Oh of course, the taylor series: Magic wand of physicists

spuckhafte