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Sorry if this question has been asked before. I have done some googling but with no luck. I'm not sure how to explain exactly so I'll just write the maths.

Is this statement true?

$$\int_{-\infty}^{\infty} x^2*e^{-(x-b)^2}dx = \frac{\sqrt\pi}{2}$$

Or is this statement true? $$\int_{-\infty}^{\infty} (x-b)^2*e^{-(x-b)^2}dx = \frac{\sqrt\pi}{2}$$

Or are neither? Basically does the index power have to match what the multiplying variable is or not? If that makes sense.

Thanks in advance!

Jess Miller
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    Neither. Both integrals are divergent. – an4s Apr 12 '20 at 04:01
  • Thank you for the quick response! Sorry though I just realised I forgot my negatives while trying to work out the math's formatting. Are they still divergent if that is the case? I have edited it so it displays correctly. – Jess Miller Apr 12 '20 at 04:10
  • No, in that case neither integrals are divergent and $\displaystyle\int_{-\infty}^{\infty}(x - b)^2e^{-(x - b)^2},\mathrm dx = \dfrac{\sqrt\pi}2$. – an4s Apr 12 '20 at 04:17
  • Thank you so much! – Jess Miller Apr 12 '20 at 04:19

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