I Integration leading to ERFI solutions

[Oaxaca]

I am attempting to normalize a wave function and need to integrate $\int A^2*e^{(\lambda^2x^2)} dx$ going from -inf to +inf. I tried to integrate this on Wolfram Alpha and this was the result. Upon integrating with the parameters the solution is as such. How does the erfi get removed? Do I need to be familiar with the Dawson function?

Thank you for any help!

 

[JorisL]

If you look at the condition for the case when there is no inverse error function (erfi) you'll see that they require
$$Re(\lambda^2)<0$$

This means that we can choose $\lambda=i C$ (for simplicity).

Do you see what happens in that case?