# Integral involving e^(x^2)

i am solving a problem that involves taking the integral of an exponential to the power of -x^2. I would have no problem solving this integral if the limits were 0 to infinity but the limits i am solving for are an arbitrary a to infinity. Can anybody help?

## Answers and Replies

i am solving a problem that involves taking the integral of an exponential to the power of -x^2. I would have no problem solving this integral if the limits were 0 to infinity but the limits i am solving for are an arbitrary a to infinity. Can anybody help?
Sounds like a gaussian function:
http://en.wikipedia.org/wiki/Normal_distribution

The anti-derivative is the error function, which is nonelementary.

that verifies what i was thinking but i am still having trouble going about solving it. I think I am just not sure where to start. Thanks though at least I know I am not completely off track

D H
Staff Emeritus
Science Advisor
You can't solve it, in terms of elementary functions, that is. As Tac-Tics already said, the error function is non-elementary.