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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

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

Substitute back

u = sin (t)

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

Add a constant to the solution

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

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