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

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

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integral of cos^6(θ)sin(θ)

\int cos^{6} (θ) sin (θ) d θ

- \frac{cos ^{7} ( θ )}{7} + C

Solution steps

\int cos^{6} (θ) sin (θ) d θ

Apply u-substitution

: \int - u^{6} d u

= \int - u^{6} d u

Take the constant out:

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

= - \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

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

Substitute back

u = cos (θ)

= - \frac{cos ^{7} ( θ )}{7}

Add a constant to the solution

= - \frac{cos ^{7} ( θ )}{7} + C

\frac{\partial}{\partial y} (y^{3} sin (2 x))

\frac{d y}{d x} = 4

\frac{d}{d x} (4 x^{\frac{3}{5}})

\int_{1}^{2} (- 12 x + 6) d x

y^{^{'}} = \frac{x ^{2} - y ^{2}}{x y}, y (2) = 3

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