Explanation Given: The expression is ∫ x 3 ln x d x . Formula used: Write the integration by part formula: ∫ u d v = u v − ∫ v d u Calculation: Consider the following expression: ∫ x 3 ln x d x Assume u = ln x . Determine d u by take a derivative: d u = 1 x d x Assume d v = x 3 d x . Determine v by taking an anti-derivative. ∫ d v = ∫ x 3 d x v = 1 4 x 4 Recall the integration by part formula: ∫ u d v = u v − ∫ v d u Substitute ln x for u , x 3 d x for d v , 1 4 x 4 for v and 1 x d x for d u

Pearson eText for Mathematics with Applications In the Management, Natural, and Social Sciences -- Instant Access (Pearson+)

12th Edition

ISBN: 9780137504381

Author: Margaret Lial, Thomas Hungerford

Publisher: PEARSON+

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Chapter 13.3, Problem 27E

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To calculate: The value of the expression ∫x3lnxdx by using the integration by parts.

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Chapter 13.3, Problem 26E

Chapter 13.3, Problem 28E

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Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

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The value of the expression ∫ x 3 ln x d x by using the integration by parts.

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