JEE Main 202226 Jul, Evening shiftMathematicsHardIntegral Calculus369× since 2002 The integral ∫(1−13)(cosx−sinx)(1+23sin2x)dx is equal to \text { The integral } \int \frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}} \sin 2 x\right)} d x \text { is equal to } The integral ∫(1+32sin2x)(1−31)(cosx−sinx)dx is equal to AOption A. 12loge∣tan(x2+π12)tan(x2+π6)∣+C\frac{1}{2} \log _{e}\left|\frac{\tan \left(\frac{x}{2}+\frac{\pi}{12}\right)}{\tan \left(\frac{x}{2}+\frac{\pi}{6}\right)}\right|+C21logetan(2x+6π)tan(2x+12π)+CBOption B. 12loge∣tan(x2+π6)tan(x2+π3)∣+C\frac{1}{2} \log _{e}\left|\frac{\tan \left(\frac{x}{2}+\frac{\pi}{6}\right)}{\tan \left(\frac{x}{2}+\frac{\pi}{3}\right)}\right|+C21logetan(2x+3π)tan(2x+6π)+CCOption C. loge∣tan(x2+π6)tan(x2+π12)∣+C\log _{e}\left|\frac{\tan \left(\frac{x}{2}+\frac{\pi}{6}\right)}{\tan \left(\frac{x}{2}+\frac{\pi}{12}\right)}\right|+Clogetan(2x+12π)tan(2x+6π)+CDOption D. 12loge∣tan(x2−π12)tan(x2−π6)∣+C\frac{1}{2} \log _{e}\left|\frac{\tan \left(\frac{x}{2}-\frac{\pi}{12}\right)}{\tan \left(\frac{x}{2}-\frac{\pi}{6}\right)}\right|+C21logetan(2x−6π)tan(2x−12π)+CCheckSkip · show solution
