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

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

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

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

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

Solution steps

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

y^{^{''}} + 9 y = cos (3 x) + sin (3 x)

y^{^{'}} = \frac{6 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

2 x^{3} + 2 x - 1

z \to - 1 + 2 i lim (\frac{z}{z + 1 + 2 i})

\frac{d}{d x} (- \frac{x ^{2}}{y ^{2}})

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