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

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

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

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

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

Solution steps

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

Simplify

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

Apply u-substitution

: \int - u^{2} d u

= \int - u^{2} d u

Take the constant out:

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

= - \int u^{2} d u

Apply the Power Rule

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

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

Substitute back

u = cos (x)

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

Add a constant to the solution

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

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

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

\frac{3}{x - 6}

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 4, y^{^{'}} (0) = - 3

\int \frac{4 x}{4 x ^{2} - 12 x + 13} d x

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