What is the integral of (1-cos(x))^5sin(x) ?

The integral of (1-cos(x))^5sin(x) is ((1-cos(x))^6)/6+C

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integral of (1-cos(x))^5sin(x)

\int (1 - cos (x))^{5} sin (x) d x

\frac{( 1 - cos ( x ) ) ^{6}}{6} + C

Solution steps

\int (1 - cos (x))^{5} sin (x) d x

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{u ^{6}}{6}

Substitute back

u = 1 - cos (x)

= \frac{( 1 - cos ( x ) ) ^{6}}{6}

Add a constant to the solution

= \frac{( 1 - cos ( x ) ) ^{6}}{6} + C

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\int \frac{x ^{2} + 9 x + 18}{x + 3} d x

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\int x e^{- x^{2} + 1} d x

What is the integral of (1-cos(x))^5sin(x) ?
The integral of (1-cos(x))^5sin(x) is ((1-cos(x))^6)/6+C