What is the antiderivative of #e^(x^2)#?

1 Answer
Apr 10, 2016

Answer:

It can be written #2/sqrtpi "erfi"(x)#. Where #"erfi"(x)# is called the imaginary error function at #x#

Explanation:

The function #e^(x^2)# has an antiderivative, but there is no nice way to express it using elementary function.

Saying that the antiderivative of #e^(x^2)# is #2/sqrtpi# times the imaginary error function at #x# doesn't help the intro student much, but that's what it is.