What is the integral of cos^5(θ)sin(θ) ?

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

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integral of cos^5(θ)sin(θ)

\int cos^{5} (θ) sin (θ) d θ

- \frac{cos ^{6} ( θ )}{6} + C

Solution steps

\int cos^{5} (θ) sin (θ) d θ

Apply u-substitution

: \int - u^{5} d u

= \int - u^{5} d u

Take the constant out:

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

= - \int u^{5} d u

Apply the Power Rule

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

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

Substitute back

u = cos (θ)

= - \frac{cos ^{6} ( θ )}{6}

Add a constant to the solution

= - \frac{cos ^{6} ( θ )}{6} + C

y = x, y = 2 x 49 - x^{2}

y^{^{''}} + 25 y = 0, y (π) = 3, y^{^{'}} (π) = - 3

\int_{0}^{4} (- x^{2} + 4 x) d x

(1) (- 1.5)

y^{^{'}} + 3 y = 2 e^{- x}

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