If n is a positive integer, prove that 1 0 (ln x) n dx (1) n n ...

n is a positive integer so Thus by repeated application of lHospita ...

If n is a positive integer, prove that 1 0 (ln x) n dx = (1)

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If n is a positive integer, prove that ∫¹₀ (ln x)ⁿ dx = (–1)ⁿn!.

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Calculus Early Transcendentals

ISBN: 9781337613927

9th Edition

Authors: James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin

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Question Posted: Jan 13, 2021 05:56 AM

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If n is a positive integer, prove that 1 0 (ln x) n dx = (1)

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Calculus Early Transcendentals

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