dx-1-sin-x-

Question Number 97526 by student work last updated on 08/Jun/20

\int \frac{dx}{1 + \sin x} = ?

Commented by bobhans last updated on 08/Jun/20

\frac{1}{1 + \sin x} \times \frac{1 - \sin x}{1 - \sin x} = \frac{1 - \sin x}{\cos^{2} x}

\int \sec^{2} x - \sec x \tan x dx = \tan x - \sec x + c

Answered by smridha last updated on 08/Jun/20

\int \frac{{s e c}^{2} \frac{x}{2} d x}{1 + {t a n}^{2} \frac{x}{2} + 2 t a n \frac{x}{2}} d x

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

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