What is the integral of cos(θ)sin^8(θ) ?

The integral of cos(θ)sin^8(θ) is (sin^9(θ))/9+C

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integral of cos(θ)sin^8(θ)

\int cos (θ) sin^{8} (θ) d θ

\frac{sin ^{9} ( θ )}{9} + C

Solution steps

\int cos (θ) sin^{8} (θ) d θ

Apply u-substitution

: \int u^{8} d u

= \int u^{8} d u

Apply the Power Rule

: \frac{u ^{9}}{9}

= \frac{u ^{9}}{9}

Substitute back

u = sin (θ)

= \frac{sin ^{9} ( θ )}{9}

Add a constant to the solution

= \frac{sin ^{9} ( θ )}{9} + C

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What is the integral of cos(θ)sin^8(θ) ?
The integral of cos(θ)sin^8(θ) is (sin^9(θ))/9+C