Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 4 - Integration - 4.2 The Indefinite Integral - Exercises Set 4.2 - Page 279: 32


$$\frac{1}{2}\tan x +c$$

Work Step by Step

Given$$\int \frac{dx}{1+\cos 2x}$$ Since $$\cos 2x=2\cos^2x-1$$ \begin{align*} \int \frac{dx}{1+\cos 2x} &=\int \frac{dx}{2\cos^2x}\\ &=\frac{1}{2}\int \sec^2 xdx\\ &=\frac{1}{2}\tan x +c \end{align*}
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