What is the integral of 1/(sin^2(w)sqrt(1-cot(w))) ?

The integral of 1/(sin^2(w)sqrt(1-cot(w))) is 2sqrt(1-cot(w))+C

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integral of 1/(sin^2(w)sqrt(1-cot(w)))

\int \frac{1}{sin ^{2} ( w ) 1 - cot ( w )} d w

2 1 - cot (w) + C

Solution steps

\int \frac{1}{sin ^{2} ( w ) 1 - cot ( w )} d w

Apply u-substitution

: \int - \frac{1}{1 - u} d u

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply u-substitution

: \int - \frac{1}{v} d v

= - \int - \frac{1}{v} d v

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- \int \frac{1}{v} d v)

Apply the Power Rule

: 2 v^{\frac{1}{2}}

= - (- 2 v^{\frac{1}{2}})

Substitute back

= - (- 2 (1 - cot (w))^{\frac{1}{2}})

Simplify

- (- 2 (1 - cot (w))^{\frac{1}{2}}) : 2 1 - cot (w)

= 2 1 - cot (w)

Add a constant to the solution

= 2 1 - cot (w) + C

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What is the integral of 1/(sin^2(w)sqrt(1-cot(w))) ?
The integral of 1/(sin^2(w)sqrt(1-cot(w))) is 2sqrt(1-cot(w))+C