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) 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{e ^{y^{2}}}{( 2 y + 1 ) ^{5}}

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

\int \frac{( 1 - 2 x )}{x ^{2}} d x

\frac{d}{d x} (\frac{1}{4} e^{- x} + e^{x})

f (x) = x x + 1

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