Calculating $\int\sin(x)\ln(\sin(x))\, \mathrm{d}x$ I was solving indefinite integrals for preparing me to a math test but I found a very hard one I'm not able to solve. It is
$$\int \sin(x)\ln(\sin(x))\, \mathrm{d}x$$
I tried to solve it by substitution but I wasn't able to express the $dx$ with a smart method. The only way I can think to solve it is by parts but it would be too much difficult in my opinion.
I hope you can help me even with an advice, thanks in advance.

Hint
Use integration by parts and call: $u=\log (\sin x)$ and $dv=\sin x dx$, so:
$$\int \sin x \log (\sin x)dx=\int u dv=uv-\int v du$$
where, $v=-\cos x$ and $du=\cos x\cdot \frac{1}{\sin x}$
