Relationship between integral of x*log(sin(x)), and Apéry's constant, pi, and logarithm
From specialfunctionswiki
Theorem
The following formula holds: $$\displaystyle\int_0^{\frac{\pi}{2}} x \log(\sin(x)) dx = \dfrac{7}{16}\zeta(3) - \dfrac{\pi^2}{8} \log(2).$$
