Question

The integral $\int \frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}} \sin 2 x\right)} d x$ is equal to

Accepted Answer

$\frac{1}{2} \log _e\left|\frac{	an \left(\frac{x}{2}+\frac{\pi}{12}ight)}{	an \left(\frac{x}{2}+\frac{\pi}{6}ight)}ight|+C$

Answer

$\frac{1}{2} \log _e\left|\frac{	an \left(\frac{x}{2}+\frac{x}{6}ight)}{	an \left(\frac{x}{2}+\frac{\pi}{3}ight)}ight|+C$

Answer

$\log _e\left|\frac{	an \left(\frac{x}{2}+\frac{\pi}{6}ight)}{	an \left(\frac{x}{2}+\frac{\pi}{12}ight)}ight|+C$

Answer

$\frac{1}{2} \log _e\left|\frac{	an \left(\frac{x}{2}-\frac{\pi}{12}ight)}{	an \left(\frac{x}{2}-\frac{\pi}{6}ight)}ight|+C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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