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

Dec 3, 2016

Answer:

It doesn't have one, unless you allow the use of the error function $e r f \left(x\right)$ but that is a bit circular because the definition of $e r f \left(x\right)$ is $\left(\frac{2}{\sqrt{\pi}}\right) {\int}_{-} {\infty}^{x} {e}^{- {t}^{2}} \mathrm{dt}$.

Explanation:

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