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 |}.