What is the integral of (cot(θ))/(sqrt(sin(θ))) ?

The integral of (cot(θ))/(sqrt(sin(θ))) is -2/(sqrt(sin(θ)))+C

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integral of (cot(θ))/(sqrt(sin(θ)))

\int \frac{cot ( θ )}{sin ( θ )} d θ

- \frac{2}{sin ( θ )} + C

Solution steps

\int \frac{cot ( θ )}{sin ( θ )} d θ

Apply u-substitution

= \int \frac{1}{u u} d u

Simplify

u u : u^{\frac{3}{2}}

= \int \frac{1}{u ^{\frac{3}{2}}} d u

Apply the Power Rule

= - \frac{2}{u}

Substitute back

u = sin (θ)

= - \frac{2}{sin ( θ )}

Add a constant to the solution

= - \frac{2}{sin ( θ )} + C

What is the integral of (cot(θ))/(sqrt(sin(θ))) ?
The integral of (cot(θ))/(sqrt(sin(θ))) is -2/(sqrt(sin(θ)))+C