What is the integral of sin^7(θ)cos(θ) ?

The integral of sin^7(θ)cos(θ) is (sin^8(θ))/8+C

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integral of sin^7(θ)cos(θ)

\int sin^{7} (θ) cos (θ) d θ

\frac{sin ^{8} ( θ )}{8} + C

Solution steps

\int sin^{7} (θ) cos (θ) d θ

Apply u-substitution

: \int u^{7} d u

= \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{u ^{8}}{8}

Substitute back

u = sin (θ)

= \frac{sin ^{8} ( θ )}{8}

Add a constant to the solution

= \frac{sin ^{8} ( θ )}{8} + C

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What is the integral of sin^7(θ)cos(θ) ?
The integral of sin^7(θ)cos(θ) is (sin^8(θ))/8+C