I'm trying to find the following integral for fun:
$$\int \frac{\sin x}{\ln x}\,\mathrm dx.$$
I simply tried to convert the nominator into something log-friendly using:
$$\sin x = \frac{e^{ix}-e^{-ix}}{2i} $$
Then, I tried to change integration variable using $y = e^{ix}$ or $y = \ln x$, but neither seems to be helpful.
What is the right way to analytically wrestle with this integral?