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Find $\int \cos(\ln x) \mathrm dx$.

I started by substitution. Let $u=\ln x$, so we get $\mathrm du=\frac{1}{x} \mathrm dx$ and $x=e^{u}$. Then the integral stays like this:

$$\int \cos(u)e^{u} \mathrm du$$

But now I can't managed how to finish. I've tryed integration by parts, but it seems like there is allways an integral remainingto integrate by parts.

Can you help me? Thanks