How do I do a finite expansion of $\int e^{x^2} \, dx$?

Asked Dec 01 '15 at 01:10

Active Dec 01 '15 at 01:17

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I am looking for a way to make a finite expression of the integral of e to the x-squared. How can I go about this? $$\int e^{x^2} \, dx$$

edited Dec 01 '15 at 01:17

Leucippus

asked Dec 01 '15 at 01:10

user294826

5

Can't be done. There is no closed form expression for this indefinite integral. See https://en.wikipedia.org/wiki/Error_function and the almost identical question http://math.stackexchange.com/questions/965378/how-to-int-e-x2-dx?rq=1 – Ethan Bolker Dec 01 '15 at 01:21
2

We typically say "expressed in terms of elementary functions" instead of "finite expression" because otherwise you could just say that $\mathrm{erf}(x)$ (times some constant) is a finite expression for the antiderivative. – Christopher A. Wong Dec 01 '15 at 01:31
You have expressed this antiderivative using a finite number of symbols. Thus, you have indeed given a "finite expression" of it. – Michael Dec 01 '15 at 03:32
Can you help me with an expansion of this problem then? – user294826 Dec 01 '15 at 06:13

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