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

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

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

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

2 1 - cot (x) + C

Solution steps

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

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 (x))^{\frac{1}{2}})

Simplify

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

= 2 1 - cot (x)

Add a constant to the solution

= 2 1 - cot (x) + C

\int \frac{1}{x ^{2} + 2 x + 7} d x

\int tan^{3} (x) (sec (x))^{\frac{- 1}{2}} d x

\int \frac{- 2 x}{( x + 1 ) - x + 1} d x

\int (3 x + \frac{3}{5}) d x

\int \frac{x}{1 - x} d x

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