# ∫ Cot X √ Sin X D X - Mathematics

Sum

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

#### Solution

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

$= \int\frac{\cos x}{\sin x \sqrt{\sin x}} dx$

$= \int\frac{\cos x}{\left( \sin x \right)^\frac{3}{2}}dx$

$Let \sin x = t$

$\Rightarrow \cos x = \frac{dt}{dx}$

$\Rightarrow \text{cos x dx} = dt$

$Now, \int\frac{\cos x}{\left( \sin x \right)^\frac{3}{2}}dx$

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

$= \int t^{- \frac{3}{2}} dt$

$= \left[ \frac{t^{- \frac{3}{2} + 1}}{\frac{- 3}{2} + 1} \right] + C$

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

$= - \frac{2}{\sqrt{\sin x}} + C$

Concept: Evaluation of Simple Integrals of the Following Types and Problems
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.9 | Q 11 | Page 58