Integrate the function e^(x^2)

[lost_math]

Homework Statement

Integrate the function e^(-x^2) with definite integrals -infinity to X

Homework Equations

The Attempt at a Solution

I know that the indefinite integral of this reduces to sqrt(pi), but don't know what to do with the definite integral. Is this a known result that I can simply plug in and use?What kind of substitution can I try? FYI- this is a variation of the CDF for a normally distributed function...

 

[Gib Z]

Homework Statement

Integrate the function e^(-x^2) with definite integrals -infinity to X

Impossible in terms of elementary functions. Why not look up the error function though?

EDIT: is X independent of x? I am unclear with your notation.