41+ E^x^2 PNG. Over the entire real line. And the second derivative if you can include as well.
The expected mean e(x) :
Now then, onto the integral. We also did some work about finding expected values of functions and such, like $e(g(x))$. Integral of e^(x^2) & the imaginary error function. It looks simple enough to do by recognition as long as you're prepared to fiddle about with it.