$\int \frac{x + s i n x}{1 + c o s x} d x =$

l o g | 1 + c o s x | + C

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x t a n \frac{x}{2} + C

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- l o g | 1 + c o s x | + C

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x c o t (\frac{x}{2}) + C

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Solution

The correct option is B $x t a n \frac{x}{2} + C$
$I = \int (\frac{x}{2} s e c^{2} \frac{x}{2} + t a n \frac{x}{2}) d x = x t a n \frac{x}{2} - \int t a n \frac{x}{2} d x + \int t a n \frac{x}{2} d x I = x t a n \frac{x}{2}$

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