Question

integral of cosx / 1+cosx​

Answer 1

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Answer 2

Answer:

$→\int \frac{ \cos(x) }{1 + \cos(x) } dx \\ = \int \frac{ \cos(x) + 1 - 1 }{1 + \cos(x) } dx \\ = \int \frac{1 + \cos(x) }{1 + cos(x)} dx - \int \frac{1}{1 + \cos(x) } dx \\ = \int dx - \int \frac{1}{2 { \cos}^{2}( \frac{x}{2} ) } dx \\ = \int dx- \frac{1}{2} \int \sec ^{2} ( \frac{x}{2} ) dx \\ = x - \frac{1}{2} ( \frac{ \tan( \frac{x}{2} ) }{ \frac{1}{2} } ) + C \\ = x - \tan( \frac{x}{2} ) + C$

• x-tan(x/2)+C is the right answer.