What is the integral of (sin(x))/(sqrt((1-cos(x)))) ?

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

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integral of (sin(x))/(sqrt((1-cos(x))))

\int \frac{sin ( x )}{( 1 - cos ( x ) )} d x

2 1 - cos (x) + C

Solution steps

\int \frac{sin ( x )}{1 - cos ( x )} d x

Apply u-substitution

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

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

Apply the Power Rule

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

= 2 u^{\frac{1}{2}}

Substitute back

u = 1 - cos (x)

= 2 (1 - cos (x))^{\frac{1}{2}}

Apply radical rule:

= 2 1 - cos (x)

Add a constant to the solution

= 2 1 - cos (x) + C

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