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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

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

Substitute back

u = sin (x)

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{2 x ^{2} - 1}{x ^{2} - 3})

\int 20 x^{3} + 12 x^{2} + 4 d x

\frac{\partial}{\partial x} (y^{2} x + y)

\frac{d y}{d x} + y^{3} x + 5 y = 0

6 x (\frac{d y}{d x}) = 2 x e^{x} - 6 y + 6 x^{2}

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