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Deriving the (open-form) integral of e^(x^2)

WARNING: Math content ahead!

Although e^(x^2) does not have an antiderivative that can be written finitely as a bunch of elementary functions smooshed together (aka a closed-form antiderivative), it DOES have an open-form antiderivative. This derivation starts with the power series for e^x, and substitutes in x^2 for x, yielding the power series for e^(x^2). This can be integrated term by term, yielding the power series form of the most general antiderivative of e^(x^2).

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