Computing Some Integrals via Gauss Integral $ \displaystyle\int_{-\infty }^\infty e^{-\frac{1}{2} x^2} \; dx $ 
and 
$ \displaystyle\int_{-\infty }^\infty x^{2}e^{-\frac{1}{2}x^2} \; dx $ 
how i compute these integrals via Gauss Integral?

Make the substitution $x = \sqrt{2}\  t$ in both, and use integration by parts in the second, by writing 
$$2t^2 e^{-t^2} = -t \times \frac{d e^{-t^2}}{dt}$$
