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

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

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

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

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

Solution steps

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

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 (z)

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

Add a constant to the solution

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

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What is the integral of sin(z)sqrt(1-cos(z)) ?
The integral of sin(z)sqrt(1-cos(z)) is 2/3 (1-cos(z))^{3/2}+C