Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.6 Strategies for Integration - Exercises - Page 431: 53


$$ 9\tan x -\frac{11}{2}x+\frac{1}{4}\sin 2x+C$$

Work Step by Step

Given $$\int(3 \sec x-\cos x)^{2} d x$$ Then \begin{align*} \int(3 \sec x-\cos x)^{2} d x&=\int(9 \sec^2 x-6+\cos^2 x) d x\\ &= \int(9 \sec^2 x-6+\frac{1}{2}+\frac{1}{2}\cos2 x) d x\\ &= 9\tan x -\frac{11}{2}x+\frac{1}{4}\sin 2x+C \end{align*}
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