Question

Integrate the function: $\frac {cos \ x}{\sqrt {1+ sin \ x}}$

Answer 1

$Let \ 1+sin\ x = t$
$∴ cos \ x \ dx = dt$
⇒ ∫$$\frac {cos \ x}{\sqrt {1+ sin \ x}}dx = $∫dt/\sqrt t$
=$\frac {t^{\frac 12}}{\frac 12}+C$
=$2\sqrt t +C$
=$2\sqrt {1 + sin x} +C$