Answer
$$\frac{4}{5}\sec ^{\frac{5}{4}}\left(x\right)+C$$
Work Step by Step
\begin{align*}
\int \tan x \sec ^{5 / 4} x d x&=\int \sec ^{1 / 4} x \tan x \sec x d x\\
&=\frac{4}{5}\sec ^{\frac{5}{4}}\left(x\right)+C
\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 - 8.6 Strategies for Integration - Exercises - Page 431: 52
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