What is the integral of cos(t)sin^3(t) ?

The integral of cos(t)sin^3(t) is (sin^4(t))/4+C

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integral of cos(t)sin^3(t)

\int cos (t) sin^{3} (t) d t

\frac{sin ^{4} ( t )}{4} + C

Solution steps

\int cos (t) sin^{3} (t) d t

Apply u-substitution

= \int u^{3} d u

Apply the Power Rule

= \frac{u ^{4}}{4}

Substitute back

u = sin (t)

= \frac{sin ^{4} ( t )}{4}

Add a constant to the solution

= \frac{sin ^{4} ( t )}{4} + C

What is the integral of cos(t)sin^3(t) ?
The integral of cos(t)sin^3(t) is (sin^4(t))/4+C