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

The integral of-cos^2(x)sin(x) is 1/3 cos^3(x)+C

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

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

\frac{1}{3} cos^{3} (x) + C

Solution steps

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

Take the constant out:

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

= - \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})

Simplify

- (- \frac{cos ^{3} ( x )}{3}) : \frac{1}{3} cos^{3} (x)

= \frac{1}{3} cos^{3} (x)

Add a constant to the solution

= \frac{1}{3} cos^{3} (x) + C

\int (5 cos (x) + 4 sin (x)) d x

\frac{d}{d x} (\frac{x}{tan ( 3 x - 1 )})

\int \frac{ln ( y )}{x y} d y

n = 1 \sum \infty \frac{1}{2 n ^{3}}

\frac{\partial}{\partial x} (x - 2 x - \frac{2}{3} y)

What is the integral of-cos^2(x)sin(x) ?
The integral of-cos^2(x)sin(x) is 1/3 cos^3(x)+C