Integrate $e^{x^2} dx$ I tried $u$-substiution with $u = x^2$ but that leaves me with $x$ values and not a simpler function to integrate.Is there a better way to integrate? 

The result of integration can't be expressed using elementary functions. Such integrals can be calculated only on a defined segment and sometimes only numerically. In other words, there's no such function expressed as a trigonometrical, degree, exponential, logarithmic function, their sum, difference, multiplication, division or composition which derivative equals $e^{x^2}$.
