Integrate

the indefinite integral ∫e^x2dx is not integrable.

How do u find out whether some thing is integrable or not?

@b555
It is not correct to say (#2) that it is not integrable. Indeed, let
F(x)=\int_0^xe^{t^2}\ \mathrm dt
It is easy to see that
F'(x)=e^{x^2}
so that F(x) is the antiderivative of e^x2. The point is that the integral cannot be expressed in terms of the elementary function. But that's not the same as being not integrable.