Can You Solve This Integral?

[Frankww]

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

 

[Doc Al]

Try http://integrals.wolfram.com/index.jsp"

 

[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
$\sqrt{\pi/|\lambda |}$.