Answer
$$
\int \sec^2(\cos x) \sin xdx
=-\tan (\cos x) +c
$$
Work Step by Step
Since $ u= \cos x $, then $ du=-\sin x dx $ and hence, $$
\int \sec^2(\cos x) \sin xdx =-\int \sec^2 u d u= -\tan u +c\\
=-\tan (\cos x) +c.
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 22
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