What is the integral of sin^2(t)cos(t) ?

The integral of sin^2(t)cos(t) is (sin^3(t))/3+C

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integral of sin^2(t)cos(t)

\int sin^{2} (t) cos (t) d t

\frac{sin ^{3} ( t )}{3} + C

Solution steps

\int sin^{2} (t) cos (t) d t

Apply u-substitution

= \int u^{2} d u

Apply the Power Rule

= \frac{u ^{3}}{3}

Substitute back

u = sin (t)

= \frac{sin ^{3} ( t )}{3}

Add a constant to the solution

= \frac{sin ^{3} ( t )}{3} + C

What is the integral of sin^2(t)cos(t) ?
The integral of sin^2(t)cos(t) is (sin^3(t))/3+C