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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int v^{2} d v

= \int v^{2} d v

Apply the Power Rule

: \frac{v ^{3}}{3}

= \frac{v ^{3}}{3}

Substitute back

v = sin (u)

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

Add a constant to the solution

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

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