$I_1= \int \limits _0^{\pi} x \log \sin x dx;\; I_2=\int \limits_0^{\pi} \log \sin x dx . $ find $\large\frac{I_1}{I_2}$=?

Question

\[\begin {array} {1 1} (a)\;\frac{\pi}{2} \\ (b)\;\frac{\pi}{4} \\ (c)\;\frac{\pi}{6} \\ (d)\;\frac{\pi}{8} \end {array}\]