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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

\frac{d}{d x} ((ln (x))^{\frac{1}{x}})

\int_{0}^{1} (x - \frac{1}{2})^{2} d x

\frac{d y}{d t} - 2 y = 3 e^{- 2 t}

\frac{d}{d x} y = (3 x + 2) (5 x^{2} + 4)

\int \frac{x}{x - 1 + 1} d x

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