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

The integral of sin(x)sqrt(1-cos(x)) is 2/3 (1-cos(x))^{3/2}+C

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

integral

sin (x) 1 - cos (x)

\frac{2}{3} (1 - cos (x))^{\frac{3}{2}} + C

Solution steps

\int sin (x) 1 - cos (x) d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = 1 - cos (x)

= \frac{2}{3} (1 - cos (x))^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (1 - cos (x))^{\frac{3}{2}} + 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 2/3 (1-cos(x))^{3/2}+C