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

The integral of 2sin^4(x)cos(x) is 2/5 sin^5(x)+C

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

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

\frac{2}{5} sin^{5} (x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int u^{4} d u

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

Apply the Power Rule

: \frac{u ^{5}}{5}

= 2 \cdot \frac{u ^{5}}{5}

Substitute back

u = sin (x)

= 2 \cdot \frac{sin ^{5} ( x )}{5}

Simplify

2 \cdot \frac{sin ^{5} ( x )}{5} : \frac{2}{5} sin^{5} (x)

= \frac{2}{5} sin^{5} (x)

Add a constant to the solution

= \frac{2}{5} sin^{5} (x) + C

\frac{\partial}{\partial x} (2 x e^{3 x y})

(sin (x) cos (y)) d x + (cos (x) sin (y)) d y = 0

- x^{4} - 6 x^{3} + 8 x - 6

\frac{d}{d x} (x^{2} arctan (x^{3}))

x^{3} + 4 x^{2} + 7 x + 1

What is the integral of 2sin^4(x)cos(x) ?
The integral of 2sin^4(x)cos(x) is 2/5 sin^5(x)+C