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[tex] \frac{1}{4 \pi \sigma^2} \int_{-\infty}^{\infty} x^2 e^{-\frac{x^2}{2\sigma^2}} [/tex]

we know that

[tex] \int_{-\infty}^{\infty} e^{-\frac{x^2}{2\sigma^2}} = \sqrt{2 \pi \sigma^2} [/tex]

and then differentiate both sides wrt sigma

[tex] \int_{-\infty}^{\infty} x^2 e^{-\frac{x^2}{2\sigma^2}} = \sigma^3 \sqrt{2 \pi} [/tex]

sib the third into the first

[tex] \frac{1}{4 \pi \sigma^2} \sigma^3 \sqrt{2 \pi} [/tex]

[tex] \frac{\sigma \sqrt{2 \pi}}{4 \pi} [/tex]

something is wrong .. where did i go wrong ... pelase help :(

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# More integration

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