Explanation Given information: The integral is given as ∫ x − 1 / 5 sec ( x 4 / 5 ) tan ( x 4 / 5 ) d x . Formula used: When a substitution is performed using differentials the change of variable formula is used. ∫ f ( u ( x ) ) u ' ( x ) d x = ∫ f ( u ) d u The power rule of indefinite integrals. ∫ x n d x = x n + 1 n + 1 + C when n ≠ ( − 1 ) . Calculation: First, we have to choose a proper substitution to change the variable. Suppose that u = sec ( x 4 / 5 ) , The derivative of u is, d u d x = d sec ( x 4 / 5 ) d x = sec ( x 4 / 5 ) tan ( x 4 / 5 ) × 4 5 x 4 5 − 1 d u d x = 4 5 x − 1 5 sec ( x 4 / 5 ) tan ( x 4 / 5 ) d u = 4 5 x − 1 5 sec ( x 4 / 5 ) tan ( x 4 / 5 ) d x Using this result, we can perform the integral as, ∫ x − 1 / 5 sec ( x

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 5.7, Problem 56E

To determine

The integral ∫x −1/5sec( x 4/5 )tan( x 4/5 ) dx .

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Chapter 5.7, Problem 55E

Chapter 5.7, Problem 57E

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Chapter 5 Solutions

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The integral ∫ x − 1 / 5 sec ( x 4 / 5 ) tan ( x 4 / 5 ) d x .

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The integral ∫x −1/5sec( x 4/5 )tan( x 4/5 ) dx .

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Chapter 5 Solutions