What is the integral of (sin(x))^5cos(x) ?

The integral of (sin(x))^5cos(x) is (sin^6(x))/6+C

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integral of (sin(x))^5cos(x)

\int (sin (x))^{5} cos (x) d x

\frac{sin ^{6} ( x )}{6} + C

Solution steps

\int (sin (x))^{5} cos (x) d x

Simplify

= \int sin^{5} (x) cos (x) d x

Apply u-substitution

= \int u^{5} d u

Apply the Power Rule

= \frac{u ^{6}}{6}

Substitute back

u = sin (x)

= \frac{sin ^{6} ( x )}{6}

Add a constant to the solution

= \frac{sin ^{6} ( x )}{6} + C

What is the integral of (sin(x))^5cos(x) ?
The integral of (sin(x))^5cos(x) is (sin^6(x))/6+C