Question

Integrate 1+cosx/1-cosx

Answer 1

I=intefration of (1+cosx)/(1-cosx)
=integration of cos^2x/sin^2x
=integration of tan^2x
=integration sec^2x - 1
=tanx - x 

Answer 2

Answer:

$→ \int \frac{1 + \cos(x) }{1 - \cos(x) } dx \\ = \int \frac{2 \cos^{2} ( \frac{x}{2} ) }{2 \sin^{2} ( \frac{x}{2} ) } dx \\ = \int \cot^{2} ( \frac{x}{2} ) dx \\ = \int( \cosec^{2} ( \frac{x}{2} ) - 1)dx \\ = \int cosec^{2} ( \frac{x}{2} )dx - \int dx \\ = \frac{ - \cot( \frac{x}{2} ) }{ \frac{1}{2} } - x +C\\ = - 2 \cot( \frac{x}{2} ) - x + C$

• -2cot(x/2)-x+C is the right answer.