Question

The integral $\int \sqrt{ 1 + 2 \cot \, x (cosec \, x + \cot \, x) } dx \, \left( 0 < x < \frac{\pi}{2} \right)$ is equal to :
(where $C$ is a constant of integration)

• A. $4 \log\left(\sin \frac{x}{2}\right) + C $
• B. $2 \log\left(\sin \frac{x}{2}\right) + C $
• C. $2 \log\left(\cos\frac{x}{2}\right) + C $
• D. $4 \log\left(\cos\frac{x}{2}\right) + C $

Answer 1

Answer: (B)

$\int\left(\sqrt{+2cot x cos ecx + cos ec^{2}x + cot x}\right)dx$
$\int cos | x + cot x | dx$
$\int\left(cos ec + cot x\right)dx$
$\int cosec dx$
$2log\left(log\left(x_{2} \right) + c\right)$