What is the integral of 2cos^3(x)sin(x) ?

The integral of 2cos^3(x)sin(x) is -1/2 cos^4(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2cos^3(x)sin(x)

\int 2 cos^{3} (x) sin (x) d x

- \frac{1}{2} cos^{4} (x) + C

Solution steps

\int 2 cos^{3} (x) sin (x) d x

Take the constant out:

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

= 2 \cdot \int cos^{3} (x) sin (x) d x

Apply u-substitution

: \int - u^{3} d u

= 2 \cdot \int - u^{3} d u

Take the constant out:

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

= 2 (- \int u^{3} d u)

Apply the Power Rule

: \frac{u ^{4}}{4}

= 2 (- \frac{u ^{4}}{4})

Substitute back

u = cos (x)

= 2 (- \frac{cos ^{4} ( x )}{4})

Simplify

2 (- \frac{cos ^{4} ( x )}{4}) : - \frac{1}{2} cos^{4} (x)

= - \frac{1}{2} cos^{4} (x)

Add a constant to the solution

= - \frac{1}{2} cos^{4} (x) + C

\frac{d}{d x} (2 x x sin (x))

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

\frac{\partial}{\partial y} (5)

f (x) = - x^{2} + x, (- 1, - 2)

\int (x - 4)^{2} d x

What is the integral of 2cos^3(x)sin(x) ?
The integral of 2cos^3(x)sin(x) is -1/2 cos^4(x)+C