Answer
$$\ln \left(1+\sqrt{2}\right)$$
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*}
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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