Explanation Given: The indefinite integral, ∫ sec ( a x ) tan ( a x ) b d x . Concept Used: ∫ sec ( x ) tan ( x ) d x = sec ( x ) Sum rule of definite integrals: ∫ a b ( f ( x ) + g ( x ) ) d x = ∫ a b f ( x ) d x + ∫ a b g ( x ) d x Constant multiple rule of definite integrals: ∫ a b k f ( x ) d x = k ∫ a b f ( x ) d x , where k is a constant. d d x ( sec ( x ) ) = sec ( x ) tan ( x ) Calculation: In order to find the value of the indefinite integral ∫ sec ( a x ) tan ( a x ) b d x , use the u -substitution method

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 4.4, Problem 65S

To determine

To solve the indefinite integral ∫sec( ax)tan( ax)b dx , where a , b , and c are real numbers with a≠0, b≠0, c>0, and c≠1 .

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Chapter 4.4, Problem 64S

Chapter 4.4, Problem 66S

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To solve the indefinite integral ∫ sec ( a x ) tan ( a x ) b d x , where a , b , and c are real numbers with a ≠ 0 , b ≠ 0 , c > 0 , and c ≠ 1 .

Solution Summary: The author explains how to solve the indefinite integral with a displaystyleintmathrmsec(ax)b

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To solve the indefinite integral ∫ sec ( a x ) tan ( a x ) b d x , where a , b , and c are real numbers with a ≠ 0 , b ≠ 0 , c &gt; 0 , and c ≠ 1 .

Solution Summary: The author explains how to solve the indefinite integral with a displaystyleintmathrmsec(ax)b

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To solve the indefinite integral ∫sec( ax)tan( ax)b dx , where a , b , and c are real numbers with a≠0, b≠0, c>0, and c≠1 .

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To solve the indefinite integral ∫ sec ( a x ) tan ( a x ) b d x , where a , b , and c are real numbers with a ≠ 0 , b ≠ 0 , c > 0 , and c ≠ 1 .