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

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

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

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

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

Solution steps

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

Apply u-substitution

= \int u^{4} d u

Apply the Power Rule

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

Substitute back

u = sin (t)

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

Add a constant to the solution

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

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