Question

$Evalute\int \frac{\cot x}{\sqrt{\sin x}}dx.$

Answer 1

Solution :-

$I=\int \frac{cotx}{\sqrt{sinx}}dx$

$=\int \frac{cosx}{sinx\sqrt{sinx}}dx$

Let $sinx=t$

$\therefore cosxdx=dt$

$\therefore I=\int \frac{dt}{t^{3/2}}$

$=-2t^{-1/2}+C$

$=-\frac{2}{\sqrt{t}}+c$

$=\frac{-2}{\sqrt{sinx}}+c$