Answer
$$\frac{1}{2}\ln |x^2+1|+C$$
Work Step by Step
We integrate as follows:
\begin{align*}
\int \frac{d x}{x+x^{-1}}&=\int \frac{d x}{x+\frac{1}{x}}\\
&=\int \frac{xd x}{x^2+1}\\
&=\frac{1}{2}\ln |x^2+1|+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 - Chapter Review Exercises - Page 460: 10
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