University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 7 - Section 7.1 - The Logarithm Defined as an Integral - Exercises - Page 401: 8

Answer

$2 \sqrt {\ln (\sec x +\tan x)}+c$

Work Step by Step

Solve $\int\dfrac{\sec xdx}{\sqrt {\ln (\sec x +\tan x)}}$ Let $p=\ln (\sec x +\tan x)$ and $dp=\sec xdx$ This implies $\int\dfrac{\sec xdx}{\sqrt {\ln (\sec x +\tan x)}}=\int\dfrac{dp}{\sqrt p}=2p^{1/2}+c=2 \sqrt p+c$ Since, $p=\ln (\sec x +\tan x)$ Thus, $\int\dfrac{\sec xdx}{\sqrt {\ln (\sec x +\tan x)}}=2 \sqrt {\ln (\sec x +\tan x)}+c$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.