Explanation ∫ d x x 5 4 − 4 x 3 4 ∫ 1 x 5 4 − 4 x 3 4 d x = − ln | 1 2 x 1 4 + 1 | + ln | 1 2 x 1 4 − 1 | + C ∫ 1 x 5 4 − 4 x 3 4 d x Apply u-substitution : u = x 1 4 = ∫ 4 u 2 − 4 d u Take the constant out : ∫ a ⋅ f ( x ) d x = a ⋅ ∫ f ( x ) d x = 4 ⋅ ∫ 1 u 2 − 4 d u Apply Integral Substitution : u = 2 v = 4 ⋅ ∫ 1 2 ( v 2 − 1 ) d v Take the constant out : ∫ a ⋅ f ( x ) d x = a ⋅ ∫ f ( x ) d x = 4 ⋅ 1 2 ⋅ ∫ 1 v 2 − 1 d v v 2 − 1 = − ( − v 2 + 1 ) = 4 ⋅ 1 2 ⋅ ∫ 1 − ( − v 2 + 1 ) d v Take the constant out : ∫ a ⋅ f ( x ) d x = a ⋅ ∫ f ( x ) d x = 4 ⋅ 1 2 ( − ∫ 1 − v 2 + 1 d v ) Use the common integral : ∫ 1 − v 2 + 1 d v = ln | v + 1 | 2 − ln | v − 1 | 2 = 4

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 8.5, Problem 53E

To determine

$\int \frac{d x}{x^{\frac{5}{4}} - 4 x^{\frac{3}{4}}}$

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Chapter 8.5, Problem 52E

Chapter 8.5, Problem 54E

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Chapter 8 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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∫ d x x 5 4 − 4 x 3 4

Solution Summary: The author explains how to determine a u-substitution by taking the constant out and using the common integral.

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Chapter 8 Solutions

$\int \frac{d x}{x^{\frac{5}{4}} - 4 x^{\frac{3}{4}}}$