Explanation Formula used: Chain Rule: d y d x = d y d u ⋅ d u d x . Theorem: Substitution Rule for Indefinite Integrals. Let u = g ( x ) and g ′ ( x ) be continuous function on an interval and let f be continuous function on the corresponding range of g . On that interval ∫ f ( g ( x ) ) g ′ ( x ) = ∫ f ( u ) d u . The calculation of the ∫ d x 1 + 4 x 2 is as follows, Notice that in the integrand 1 1 + 4 x 2 , the denominator part can be written as 1 + ( 2 x ) 2 , and the numerator part of the integrand is the differentiation of the 2 x . So, assume the change of variable function u = 2 x , and differentiate with respect to x using chain rule, is 1 2 d u = d x . ∫ d x 1 + 4 x 2 = ∫ d x 1 + ( 2 x ) 2 = 1 2 ∫ d u 1 + u 2 </

Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

2nd Edition

ISBN: 9780321954329

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 5.5, Problem 29E

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To find: The value of the indefinite integral ∫dx1+4x2 by using the substitution, and then check the answer by differentiating.

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Chapter 5.5, Problem 28E

Chapter 5.5, Problem 30E

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Chapter 5 Solutions

Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

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The value of the indefinite integral ∫ d x 1 + 4 x 2 by using the substitution, and then check the answer by differentiating.

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To find: The value of the indefinite integral ∫dx1+4x2 by using the substitution, and then check the answer by differentiating.

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Chapter 5 Solutions