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

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

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

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

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

Solution steps

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

Simplify

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

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