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

The integral of cos(x)*sin^3(x) is (sin^4(x))/4+C

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integral of cos(x)*sin^3(x)

\int cos (x) \cdot sin^{3} (x) d x

\frac{sin ^{4} ( x )}{4} + C

Solution steps

\int cos (x) sin^{3} (x) d x

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

= \frac{sin ^{4} ( x )}{4}

Add a constant to the solution

= \frac{sin ^{4} ( x )}{4} + C

\frac{d}{d x} (\frac{1}{x ^{2} cos ( x )})

y^{^{'}} = 135 y x^{4}

f (x) = (5 x^{3} + 2) (3 x^{3} + 2)

n = 1 \sum \infty \frac{n - 1}{9 n - 1}

e^{- t} (t^{2} + 4 t + 5)

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