How do you find the antiderivative of $e^{- 2 x^{2}}$ $e^(-2x^2)$ ?

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How do you find the antiderivative of $e^{- 2 x^{2}}$ $e^(-2x^2)$ ?

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Answer 1 · 2016-12-03T21:21:06

It doesn't have one, unless you allow the use of the error function $e r f (x)$ $erf(x)$ but that is a bit circular because the definition of $e r f (x)$ $erf(x)$ is $(\frac{2}{\sqrt{π}}) \int_{- \infty}^{x} e^{- t^{2}} d t$ $(2/sqrt(pi))int_-oo^x e^{-t^2}dt$ .

Explanation:

A substitution like $x = \frac{t}{\sqrt{2}}$ $x=t/sqrt(2)$ looks like a good start.

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How do you find the antiderivative of $e^{- 2 x^{2}}$ $e^(-2x^2)$ ?

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How do you find the antiderivative of e−2x2e^(-2x^2)?

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How do you find the antiderivative of $e^{- 2 x^{2}}$ $e^(-2x^2)$ ?