Min-Soo Kim

In 1769, Euler proved the following result: ∫ 0 π 2 log ⁡ ( sin ⁡ θ ) ⁢ 𝑑 θ = - π 2 ⁢ log ⁡ 2 . \int_{0}^{\frac{\pi}{2}}\log(\sin\theta)\,d\theta=-\frac{\pi}{2}\log 2. In this paper, as a generalization, we evaluate the definite integrals ∫ 0 x