$\int {\frac{{dx}}{{1 + \cos x}}}$
$\int {\frac{{dx}}{{1 + \cos x}}}$
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NCERT & Exemplar
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Let $I = \int {\frac{{dx}}{{1 + \cos x}}} = \int {\frac{{dx}}{{1 + 2{{\cos }^2}\frac{x}{2} - 1}}}$
$= \frac{1}{2}\int {\frac{1}{{{{\cos }^2}\frac{x}{2}}}} dx = \frac{1}{2}\int {{{\sec }^2}} \frac{x}{2}dx$
$= \frac{1}{2} \cdot \tan \frac{x}{2} \cdot 2 + C = \tan \frac{x}{2} + C$
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