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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u^{2} d u

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

Apply the Power Rule

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

= 4 \cdot \frac{u ^{3}}{3}

Substitute back

u = sin (x)

= 4 \cdot \frac{sin ^{3} ( x )}{3}

Simplify

4 \cdot \frac{sin ^{3} ( x )}{3} : \frac{4}{3} sin^{3} (x)

= \frac{4}{3} sin^{3} (x)

Add a constant to the solution

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

\int 12 t^{2} d t

\frac{d y}{d x} = 3 y^{2} e^{3 x}, y (0) = 1

f (x) = ln (1 + 2 x^{5}), (0, 0)

f (x) = \frac{1 + 3 x}{x - 2}

\frac{d}{d x} (lo g_{b} (x))

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