Question

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

Answer 1

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

Explanation:

A substitution like `x=t/sqrt(2)` looks like a good start.