Question

\[\int\frac{\sin \left( \text{log x} \right)}{x} dx\]

Answer 1

\[\int\frac{\sin \left( \log x \right)}{x}dx\]
\[\text{Let }\log x = t\]
\[ \Rightarrow \frac{1}{x}dx = dt\]
\[Now, \int\frac{\sin \left( \log x \right)}{x}dx\]
\[ = \int\text{sin }\left( \text{t }\right) dt\]
\[ = - \text{cos} \left( \text{t }\right) + C\]
\[ = - \text{cos} \left( \text{log x} \right) + C\]