What is the integral of cos^3(θ)sin(θ) ?

The integral of cos^3(θ)sin(θ) is -(cos^4(θ))/4+C

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integral of cos^3(θ)sin(θ)

\int cos^{3} (θ) sin (θ) d θ

- \frac{cos ^{4} ( θ )}{4} + C

Solution steps

\int cos^{3} (θ) sin (θ) d θ

Apply u-substitution

: \int - u^{3} d u

= \int - u^{3} d u

Take the constant out:

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

= - \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= - \frac{u ^{4}}{4}

Substitute back

u = cos (θ)

= - \frac{cos ^{4} ( θ )}{4}

Add a constant to the solution

= - \frac{cos ^{4} ( θ )}{4} + C

x y^{^{''}} + 2 y^{^{'}} = 0

\frac{d}{d x} (\frac{1}{3} (x^{2} + 2)^{\frac{2}{3}})

n = 1 \sum \infty \frac{n ^{3}}{2 ^{n}}

\frac{d}{d x} (ln (x^{2}))

\frac{\partial}{\partial y} (x^{4} y + x z - y z^{2} - 7)

What is the integral of cos^3(θ)sin(θ) ?
The integral of cos^3(θ)sin(θ) is -(cos^4(θ))/4+C