dx-tan-x-sin-x-

Question Number 113757 by bemath last updated on 15/Sep/20

\int \frac{d x}{\tan x - \sin x} ?

Answered by bemath last updated on 15/Sep/20

Answered by Dwaipayan Shikari last updated on 15/Sep/20

2 \int \frac{1}{\frac{2 t}{1 - t^{2}} - \frac{2 t}{1 + t^{2}}} . \frac{1}{1 + t^{2}} d t t a n \frac{x}{2} = t

2 \int \frac{1}{2 t (\frac{1 + t^{2} - 1 + t^{2}}{(1 - t^{2}) (1 + t^{2})})} . \frac{1}{1 + t^{2}} d t

\int \frac{1 - t^{2}}{2 t^{3}} d t = - \frac{1}{4 t^{2}} - \frac{1}{2} l o g t + C = - \frac{1}{4 {t a n}^{2} \frac{x}{2}} - \frac{1}{2} l o g (t a n \frac{x}{2}) + C