Explanation Given information: The indefinite integral, ∫ cos 5 x sin 3 x d x Concept used: cos 2 x = 1 − sin 2 x ∫ x n d x = x n + 1 n + 1 Calculation: To evaluate the indefinite integral, first we rewrite the integrand using the Pythagorean identity. So we get ∫ cos 5 x sin 3 x d x = ∫ cos 4 x ⋅ cos x sin 3 x d x = ∫ ( cos 2 x ) 2 sin 3 x cos x d x = ∫ ( 1 − sin 2 x ) 2 sin 3 x cos x d x Now to simplify further, we use the u-substitution. So we substitute sin x = u ⇒ cos x d x = d u , So with these substitutions, above integral becomes ∫ cos 5 x sin 3 x d x = ∫ ( 1 − sin 2 x ) 2 sin 3 x cos x d x = ∫ ( 1 − u 2 ) 2 u 3 d u <

4th Edition

ISBN: 9781319279813

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 7.2, Problem 27E

To determine

To evaluate the integral ∫cos5xsin3xdx

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Chapter 7.2, Problem 26E

Chapter 7.2, Problem 28E

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Chapter 7 Solutions

CALCULUS:EARLY TRANS.-SAPLINGPLUS

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To evaluate the integral ∫ cos 5 x sin 3 x d x

Solution Summary: The author explains how to evaluate the indefinite integral by rewriting the integrand using the Pythagorean identity.

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