Calculus (3rd Edition)

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: 20


$$ \int \sec^2x\tan xdx =\frac{1}{2}\tan^2x +c $$

Work Step by Step

Since $ u=\tan x $, then $ du=\sec^2x dx $ and hence, $$ \int \sec^2x\tan xdx =\int u d u= \frac{1}{2}u^2 +c\\ =\frac{1}{2}\tan^2x +c $$
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