Question

\[\int\frac{\text{sin }\left( \text{2 + 3 log x }\right)}{x} dx\]

Answer 1

\[\int\frac{\text{sin }\left( \text{2 + 3 log x }\right)}{x} dx\]
\[\text{Let 2 + 3 }\log x = t\]
\[ \Rightarrow \frac{3}{x} = \frac{dt}{dx}\]
\[ \Rightarrow \frac{dx}{x} = \frac{dt}{3}\]
Now, \[\int\frac{\text{sin }\left( \text{2 + 3 log x }\right)}{x} dx\]
\[ = \frac{1}{3}\int \text{sin t dt}\]
\[ = \frac{1}{3} \left[ - \text{cos t }\right] + C\]
\[ = - \frac{1}{3}\text{cos }\left( \text{2 + 3 log x }\right) + C\]