I need to find the indefinite integral:
$\int \cos(\log(x)) dx$.

I've tried using u-substitution, setting $u=\log(x)$. Then I get:
$\int \cos(u)du$, where $du$ is $\frac{1}{x}dx$.

The worked solutions I can see put an $e^u$ in there as well, and I'm not really sure why. How should I go about solving this problem?

Thanks for your time.