=\int_{0}^{\frac{\pi}{2}}ln{2}dx-\int_{0}^{\frac{\pi}{2}}ln{2}dx+\int_{0}^{\frac{\pi}{2}}ln{\frac{1}{2}sin{2x}}dx=-{\frac{\pi}{2}}*ln2+\int_{0}^{\frac{\pi}{2}}ln{sin2x}dx