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,


$\begin{equation} \begin{aligned} \int \frac{\cos (\ln x)}{x} dx =& \int \cos u du \\ \\ =& \sin u + c \\ \\ =& \sin (\ln x) + c \end{aligned} \end{equation}$