# Could anybody find an INTEGRAL?

1. Nov 12, 2007

### Frankww

I've got a difficult integral, that is, $$\int_{-\infty}^{\infty} e^{\lambda x^{2}} dx$$. Could anybody find its solution?

2. Nov 12, 2007

### Staff: Mentor

Last edited by a moderator: Apr 23, 2017
3. Nov 12, 2007

### HallsofIvy

Since, for $\lambda> 0$, that is not bounded as x goes to infinity, and, if $\lambda= 0$, that is just $\int_{-\infty}^{\infty} dx$, neither of those exists.

If, however, $\lambda$ is negative, It is well known that the integral is
$\sqrt{\pi/|\lambda |}$.