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))

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

\frac{d}{d x} (5 x^{4} - 3 x^{2} + 7)

x \to \infty lim ((a)^{x})

\int \frac{1}{2 - 8 x} d x

y^{^{'}} + 3 x^{2} y = sin (x) e^{- x^{3}}, y (0) = 1

x^{3} b^{5} + y^{4} b + z^{6}

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