Explanation Given: The integral is: ∫ 1 2 x 4 ln x d x . Formula used: Use the formula 89 from the table of integrals: ∫ u n ln u d u = u n + 1 ( n + 1 ) 2 [ − 1 + ( n + 1 ) ln u ] + C ; n ≠ 1 Calculation: Consider the provided integral, ∫ 1 2 x 4 ln x d x Now, use the formula 89 to solve the integral. Let n = 4 and u = x . Then d u = d x . ∫ x 4 ln x d x = x 4 + 1 ( 4 + 1 ) 2 [ − 1 + ( 4 + 1 ) ln x ] + C =

Calculus, Early Transcendentals (Instructor's)

7th Edition

ISBN: 9781337552530

Author: Larson

Publisher: CENGAGE L

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Chapter 8.7, Problem 43E

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To calculate: The value of the definite integral ∫12x4lnxdx by the use of a table of integrals.

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Chapter 8.7, Problem 42E

Chapter 8.7, Problem 44E

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Calculus, Early Transcendentals (Instructor's)

Ch. 8.1 - CONCEPT CHECKS Integration Technique Describe how...Ch. 8.1 - CONCEPT CHECK Fitting Integrands to Basic...Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, selectthe...

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The value of the definite integral ∫ 1 2 x 4 ln x d x by the use of a table of integrals.

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To calculate: The value of the definite integral ∫12x4lnxdx by the use of a table of integrals.

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Chapter 8 Solutions