What is the integral of cos^{11}(θ)sin(θ) ?

The integral of cos^{11}(θ)sin(θ) is -(cos^{12}(θ))/(12)+C

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integral of cos^{11}(θ)sin(θ)

\int cos^{11} (θ) sin (θ) d θ

- \frac{cos ^{12} ( θ )}{12} + C

Solution steps

\int cos^{11} (θ) sin (θ) d θ

Apply u-substitution

: \int - u^{11} d u

= \int - u^{11} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{11} d u

Apply the Power Rule

: \frac{u ^{12}}{12}

= - \frac{u ^{12}}{12}

Substitute back

u = cos (θ)

= - \frac{cos ^{12} ( θ )}{12}

Add a constant to the solution

= - \frac{cos ^{12} ( θ )}{12} + C

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What is the integral of cos^{11}(θ)sin(θ) ?
The integral of cos^{11}(θ)sin(θ) is -(cos^{12}(θ))/(12)+C