What is the integral of sin^6(θ)cos(θ) ?

The integral of sin^6(θ)cos(θ) is (sin^7(θ))/7+C

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integral of sin^6(θ)cos(θ)

\int sin^{6} (θ) cos (θ) d θ

\frac{sin ^{7} ( θ )}{7} + C

Solution steps

\int sin^{6} (θ) cos (θ) d θ

Apply u-substitution

= \int u^{6} d u

Apply the Power Rule

= \frac{u ^{7}}{7}

Substitute back

u = sin (θ)

= \frac{sin ^{7} ( θ )}{7}

Add a constant to the solution

= \frac{sin ^{7} ( θ )}{7} + C

What is the integral of sin^6(θ)cos(θ) ?
The integral of sin^6(θ)cos(θ) is (sin^7(θ))/7+C