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

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

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

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

- \frac{cos ^{3} ( u )}{3} + C

Solution steps

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

Apply u-substitution

: \int - v^{2} d v

= \int - v^{2} d v

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int v^{2} d v

Apply the Power Rule

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

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

Substitute back

v = cos (u)

= - \frac{cos ^{3} ( u )}{3}

Add a constant to the solution

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

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