I = ∫ cot(x) * ln(sin(x)* dx = ∫ cos(x) / sin(x) * ln(sin(x) * dx
Substitution z = ln(sin(x)) → dz/dx = 1/sin(x) * cos(x) → dx = sin(x) / cos(x) * dz
→ I = ∫ cos(x) / sin(x) * z * sin(x) / cos(x) * dz = ∫ z dz = 1/2 * z2 + c
→ I = 1/2 * [ ln(sin(x)) ]2 + c
Gruß Wolfgang