JEE Math Practice Question

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

1. A.4 log(sin $${x \over 2}$$ ) + C
2. B.2 log(sin $${x \over 2}$$ ) + C
3. C.2 log(cos $${x \over 2}$$ ) + C
4. D.4 log(cos $${x \over 2}$$) + C