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)

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)

4 log(sin ${x \over 2}$ ) + C

2 log(sin ${x \over 2}$ ) + C

2 log(cos ${x \over 2}$ ) + C

4 log(cos ${x \over 2}$) + C

Solution

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