given $\int_{-\infty}^{+\infty} \! e^{-tx^2} \, \mathrm{d}\lambda x = \sqrt{\pi/ t} $
I have been asked to compute the moments $\int_{-\infty}^{+\infty} \! x^{2n} e^{-x^2} \, \mathrm{d}\lambda x $
how would i go about it, any help would be greatly appreciated as i can do several parts following this question but am struggling to do this initial part.
You need integration by part
$\int_{-\infty}^{+\infty} \! x^{2n} e^{-x^2} \, \mathrm{d}x = -\dfrac{1}{2}\int_{-\infty}^{+\infty} \! x^{2n-1}\, \mathrm{d} e^{-x^2} = \dfrac{2n-1}{2}\int_{-\infty}^{+\infty} \! x^{2n-2} e^{-x^2}\, \mathrm{d} x$
Repeat the same procedure to get the result