EXAMPLE 5Evaluatetan°(3x) sec*(3x) dx.If we separate one sec2(3x) factor, we can express the remainingsec?(3x) factor in terms of tangent using the identity sec?(3x) = 1 + tan?(3x).SOLUTIONWe can then evaluate the integral by substituting u =tan(3x) so thatdu =dx.| = |tan (3x) sec*(3x) dxtan (3x) sec²(3x) sec²(3x) dxtan°(3x)(1 + tan?(3x)) sec²(3x) dxdu1+du27+ C++27긁 tan®(3x) + C-|3.II

Answered: Image /qna-images/answer/ac2e37c0-2535-4f84-9016-29ce6817c7a6.jpg

Evaluate | tan (3x) sec*(3x) dx. EXAMPLE 5 If we separate one sec2(3x) factor, we can express the remaining sec?(3x) factor in terms of tangent using the identity sec2(3x) = 1 + tan?(3x). SOLUTION We can then evaluate the integral by substituting u = tan(3x) so that du = dx. | = | tan (3x) sec*(3x) dx tan (3x) sec²(3x) sec²(3x) dx tan°(3x)(1 + tan?(3x)) sec²(3x) dx du 1 + du 27 + C + + 27 긁 tan®(3x) + C -|3. II

Evaluate | tan (3x) sec(3x) dx. EXAMPLE 5 If we separate one sec2(3x) factor, we can express the remaining sec?(3x) factor in terms of tangent using the identity sec2(3x) = 1 + tan?(3x). SOLUTION We can then evaluate the integral by substituting u = tan(3x) so that du = dx. | = | tan (3x) sec(3x) dx tan (3x) sec²(3x) sec²(3x) dx tan°(3x)(1 + tan?(3x)) sec²(3x) dx du 1 + du 27 + C + + 27 긁 tan®(3x) + C -|3. II

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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