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Expectation value of x^n in a given wave function

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Consider the wave function Shi(x) = (alpha/pi)^(1/4) exp(-alpha x^2/2).

Calculate <x^n> for n = 1, 2. Can you quickly write down the result for <x^17>?

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Provided is a clear and precise solution for this problem considering the wave function Shi(x) = (alpha/pi)^(1/4) exp(-alpha x^2/2). See attachment for details.

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See attachment for further details.

Let the coefficient (α/π)1/4 = A.

Question is,

<xn> = A2

Depending on the value of n, the ...

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