Evaluate the following integrals:
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 $\mathrm{t}=\log \mathrm{x}$

$\Rightarrow \cos (\log x)+c$

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