The integral \int {(1-{1}/\sqrt{3})(\cos x-\sin x)}/{(1+\frac{2}\sqrt{3} \sin 2 x)} d x is equal to [26-Jul-2022-Shift-2]

Correct Answer is : 12loge|tan(x2+π12)tan(x2+π6)|+C

\frac{1}{2} \log _e|\binom{\tan (\frac{x}{2}+\frac{\pi}{12})}/{\tan (\frac{x}{2}+\frac{\pi}{6})}|+C

\frac{1}{2} \log _e|\binom{\tan (\frac{x}{2}+\frac{\pi}{6})}/{\tan (\frac{x}{2}+\frac{\pi}{3})}|+C

\log _e|\binom{\tan (\frac{x}{2}+\frac{\pi}{6})}/{\tan (\frac{x}{2}+\frac{\pi}{12})}|+C

\frac{1}{2} \log _e|\binom{\tan (\frac{x}{2}-\frac{\pi}{12})}/{\tan (\frac{x}{2}-\frac{\pi}{6})}|+C

JEE Mains 26-July-2022 Shift 2 Solved Paper

Section: Mathematics

Question : 19 of 90

Marks: +1, -0

The integral ∫‌

(1−

√3

)(cos‌x−sin‌x)

(1+‌

√3

‌sin‌2‌x)

dx is equal to

[26-Jul-2022-Shift-2]

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