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: 21


$$ \int x\sec^2(x^2)dx =\frac{1}{2}\tan x^2 +c $$

Work Step by Step

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