You need to know these 2 facts to follow this answer:

- (if r is an integer)

Answer

move 1 power of "a" outside the fraction

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multiply top and bottom by

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substitute v=ax, noting that

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move constants outside the integral

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The integral is now in the same form as the definition of the gamma function. i haven't written the limits in but they are still 0 and infinity, as required.

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now (since r is in integer) we can use this property of the gamma function:

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note that

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