Integration of exponential of square of x?

Answer 1

its an non integrable function

The indefinite integral of exp(x^2) dx is

1/2 * sqrt(pi) * erfi(x) + K

where erfi(x) is the imaginary error function, defined with regard to the error function as

erfi(x) = - i erf(ix)

see http://mathworld.wolfram.com/Erfi.html

Also, try wolframalpha.com, enter

exp(x^2) in the search box or

int(exp(x^2),x)

to see some plots and other info.

Answere^(x^2) is an example of a function expressible using standard functions (+, *, exp, log, atan, etc) whose integral can not be expressed in this way. In such cases we invent a name for the function defined by the interval, but it's just a name and doesn't shed any light on the function. In short, there is no intellectually satisfying answer to this question.