integration of e^(x^2)?

Answer 1

The solution to this can't be found using elementary functions. That is, you won't find a solution consisting of the functions we know (sin, cos, tan, ln, e^, a^, sqrt). Integration with the basic methods would be futile.

The actual solution consists of some variation of the error function erf(x).

Answer 2

Use integration by parts.

u = x^2 du = 2xdx
v = e^u dv = e^udu

uv - Int[ vdu]

Answer 3

[e^(x^2)]/(2x) + c