>596
　cosθ =z とおくと
　-sinθdθ = dz,
　log(sinθ) = (1/2)log(1-z^2) = (1/2)log(1-z) + (1/2)log(1+z),
　∫log(sinθ)･sinθdθ = -(1/2)∫log(1-z)dz -(1/2)∫log(1+z)dz
　　= (1/2)(1-z){log(1-z) -1} -(1/2)(1+z){log(1+z) -1} +c.
これを z=0→1 で積分。

なお、>597 は反材でつ...