Answer
\[-\cos (\ln x)+C\]
Where $C$ is constant of integration
Work Step by Step
Let \[I=\int\frac{\sin (\ln x)}{x}\,dx\]
Put \[t=\ln x\;\;\;...(1)\]
\[\Rightarrow dt=\frac{1}{x}dx\]
\[\Rightarrow I=\int \sin t\, dt\]
\[\Rightarrow I=-\cos t+C\]
Where $C$ is constant of integration
Using (1)
\[\Rightarrow I=-\cos (\ln x)+C\]
Hence, \[\int\frac{\sin (\ln x)}{x}\,dx=-\cos (\ln x)+C\]
