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!