Integrals — Class 12 Maths Solution

: Let $I = \int {\cfrac{{\cos x}}{{\sqrt {1 + \sin x} }}dx}$
Put $1 + \sin x = t$ $\Rightarrow$ $\cos x\,dx = dt$

$\therefore$ $I = \int {\cfrac{{dt}}{{{t^{1/2}}}} = \cfrac{{{t^{ - \cfrac{1}{2} + 1}}}}{{ - \cfrac{1}{2} + 1}} + C}$

$= 2{t^{1/2}} + C = 2\sqrt {1 + \sin x} + C$