Question:
Evaluate the following integrals:
$\int \frac{\sin (\log x)}{x} d x$
Solution:
Assume $\log x=t$
$d(\log x)=d t$
$\Rightarrow \frac{1}{x} d x=d t$
Substituting $\mathrm{t}$ and $\mathrm{dt}$
$\Rightarrow \int \sin t d t$
$=-\cos t+c$
But $\mathrm{t}=\log \mathrm{x}$
$\Rightarrow \cos (\log x)+c$