What is the integral of 4cos^2(x)sin(x) ?

The integral of 4cos^2(x)sin(x) is -4/3 cos^3(x)+C

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integral of 4cos^2(x)sin(x)

\int 4 cos^{2} (x) sin (x) d x

- \frac{4}{3} cos^{3} (x) + C

Solution steps

\int 4 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

= 4 \cdot \int cos^{2} (x) sin (x) d x

Apply u-substitution

: \int - u^{2} d u

= 4 \cdot \int - u^{2} d u

Take the constant out:

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

= 4 (- \int u^{2} d u)

Apply the Power Rule

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

= 4 (- \frac{u ^{3}}{3})

Substitute back

u = cos (x)

= 4 (- \frac{cos ^{3} ( x )}{3})

Simplify

4 (- \frac{cos ^{3} ( x )}{3}) : - \frac{4}{3} cos^{3} (x)

= - \frac{4}{3} cos^{3} (x)

Add a constant to the solution

= - \frac{4}{3} cos^{3} (x) + C

\int_{0}^{4} (\frac{1}{4 - x}) d x

\frac{\partial}{\partial y} (e^{x s i n (y)})

arcsin (- \frac{1}{2})

\int (x^{2})^{22} d (x^{2})^{2}

\frac{d}{d x} (tan^{x^{2}} (x))

What is the integral of 4cos^2(x)sin(x) ?
The integral of 4cos^2(x)sin(x) is -4/3 cos^3(x)+C