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

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

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

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

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

Solution steps

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

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