Explanation Given: ∫ x n e x d x = x n e x − n ∫ x n − 1 e x d x Concept used: ∫ f ( x ) g ( x ) d x = f ( x ) ∫ g ( x ) d x − ∫ [ f ′ ( x ) ⋅ ∫ g ( x ) d x ] d x Calculation: The given integral can be evaluated as ∫ x n e x d x = x n ∫ e x

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 7.2, Problem 57PS

To determine

To derive the formula ∫xn exdx=xn ex−n∫xn−1 exdx

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Chapter 7.2, Problem 56PS

Chapter 7.2, Problem 58PS

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Chapter 7 Solutions

Student's Solution and Survival Manual for Calculus

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To derive the formula ∫ x n e x d x = x n e x − n ∫ x n − 1 e x d x

Solution Summary: The author explains how the given integral can be evaluated as ldisplaystyle

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To derive the formula ∫xn exdx=xn ex−n∫xn−1 exdx

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Chapter 7 Solutions