The correct option is A 2/√( ( sin x )) I=∫cos x/sin x√( ( sin x ))dx Substitute sin x=t. #160; ∴ I=∫dt/t^3/2=∫ t^ 3/2dt= 2/√(t)= 2/√( ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Integration as Antiderivative

Solve ∫ x/√...

Question

Solve $\int \frac{cot x}{\sqrt{(sin x)}} d x$

\frac{- 2}{\sqrt{(sin x)}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{- 2}{\sqrt{(cos x)}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- 1}{\sqrt{(sin x)}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- 1}{\sqrt{(cos x)}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{- 2}{\sqrt{(sin x)}}$
$I = \int \frac{cos x}{sin x \sqrt{(sin x)}} d x$
Substitute $sin x = t .$
$∴ I = \int \frac{d t}{t^{3 / 2}} = \int t^{- 3 / 2} d t = \frac{- 2}{\sqrt{t}} = \frac{- 2}{\sqrt{(sin x)}}$

Suggest Corrections

Similar questions

\int \frac{sin x}{\sqrt{(1 + sin x)}} d x = \int (cos \frac{x}{2} + sin \frac{x}{2}) d x + \int \frac{d x}{cos (x / 2) + sin (x / 2)} .

\int_{0}^{\frac{π}{2}} \frac{sin x}{1 + cos x + sin x} d x

$\int \frac{2 s i n x}{(3 + s i n 2 x)} d x$ is equal to

\sin x + \cos x = \sqrt{2}

\sqrt{3} \cos x + \sin x = 1

\sin x + \cos x = 1

cosec x = 1 + \cot x

\int \frac{sin x + cos x}{\sqrt{1 + sin 2 x}} d x

sin x + cos x \geq 0

Join BYJU'S Learning Program