Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.2 Trigonometric Integrals - Exercises - Page 403: 53


$$\ln \left(1+\sqrt{2}\right)$$

Work Step by Step

\begin{align*} \int_{0}^{\pi/4}\frac{dx}{\cos x}&=\int_{0}^{\pi/4}\sec xdx\\ &=\ln |\sec x+\tan x|\bigg|_{0}^{\pi/4}\\ &= \ln \left(1+\sqrt{2}\right) \end{align*}
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