What is the integral of cos(x)(sin(x))^4 ?

The integral of cos(x)(sin(x))^4 is (sin^5(x))/5+C

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integral of cos(x)(sin(x))^4

\int cos (x) (sin (x))^{4} d x

\frac{sin ^{5} ( x )}{5} + C

Solution steps

\int cos (x) (sin (x))^{4} d x

Simplify

= \int sin^{4} (x) cos (x) d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = sin (x)

= \frac{sin ^{5} ( x )}{5}

Add a constant to the solution

= \frac{sin ^{5} ( x )}{5} + C

\int (300 + x)^{2} d x

(ln (x))^{2}

\int \frac{1 + x ^{3}}{x ^{2}} d x

\int π tan (π x) d x

\int \frac{( 3 ln ( x ) - 1 ) ^{4}}{x} d x

What is the integral of cos(x)(sin(x))^4 ?
The integral of cos(x)(sin(x))^4 is (sin^5(x))/5+C