Solving Indefinite Integral of Normal Equation

[Erienion]

I've been trying to integrate the following function but have gotten somewhat stuck doing it. The answer i managed to produce gave some bogan answers.

the integral in question is

$$\int e^\frac{-(x-\mu)^2}{(2\sigma)^2}$$

where $$\mu$$ and $$\sigma$$ are constants.

its part of the normal equation and I've been trying to write a program to do some calculations with it.

 

[Tide]

The integral can be expressed in terms of the error function, erf(x). Unfortunately, there is no elementary form.

 

[quasar987]

As far as I can see, by setting $y = x-\mu /2\sigma$, we get the famous $e^{-y^2}$ which doesn't have a primitive. You can however develop $e^{-y^2}$ as a Taylor serie and integrate term by term. You get the (convergant) serie of general term

$$a_n=\frac{(-1)^n x^{2n+1}}{(2n + 1)n!}$$