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

The integral of 4cos^4(x) is 4(cos^3(x)sin(x)+3/8 (x-1/4 sin(4x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4cos^4(x)

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

4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x))) + C

Solution steps

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

Simplify

cos^{4} (x) : cos^{3} (x) cos (x)

= 4 \cdot \int cos^{3} (x) cos (x) d x

Apply Integration By Parts

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

= 4 (cos^{3} (x) sin (x) - \int - 3 cos^{2} (x) sin^{2} (x) d x)

\int - 3 cos^{2} (x) sin^{2} (x) d x = - \frac{3}{8} (x - \frac{1}{4} sin (4 x))

= 4 (cos^{3} (x) sin (x) - (- \frac{3}{8} (x - \frac{1}{4} sin (4 x))))

Simplify

= 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x)))

Add a constant to the solution

= 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x))) + C

\frac{d}{d x} ((\frac{x}{4})^{2})

\frac{d}{d x} (x^{\frac{3}{5}} x^{3} + 5)

\frac{d}{d θ} (4 - θ^{2} sin (θ))

\frac{\partial}{\partial x} (\frac{1}{2 x + 3 y})

What is the integral of 4cos^4(x) ?
The integral of 4cos^4(x) is 4(cos^3(x)sin(x)+3/8 (x-1/4 sin(4x)))+C