Single Variable Calculus, Chapter 7, Review Exercises, Section Review Exercises, Problem 98

Evaluate $\displaystyle \int \frac{\cos (\ln x)}{x} dx$


$
\begin{equation}
\begin{aligned}

\text{If we let } u =& \ln x, \text{ then}
\\
\\
du =& \frac{dx}{x}

\end{aligned}
\end{equation}
$


So,


$
\begin{equation}
\begin{aligned}

\int \frac{\cos (\ln x)}{x} dx =& \int \cos u du
\\
\\
=& \sin u + c
\\
\\
=& \sin (\ln x) + c


\end{aligned}
\end{equation}
$