Answer
$$\int e^x\sec(e^x)dx=\ln|\sec(e^x)+\tan(e^x)|+C$$
Work Step by Step
$$A=\int e^x\sec(e^x)dx$$
Set $u=e^x$, we have $$du=e^xdx$$
Therefore, $$A=\int\sec udu$$ $$A=\ln|\sec u+\tan u|+C$$ $$A=\ln|\sec(e^x)+\tan(e^x)|+C$$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 7 - Practice Exercises - Page 420: 6
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