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).