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

The integral of-cos^2(2x) is -1/2 (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-cos^2(2x)

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

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

Solution steps

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

Take the constant out:

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

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

Rewrite using trig identities

= - \int \frac{1}{2} (1 + cos (4 x)) d x

Take the constant out:

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

= - \frac{1}{2} \cdot \int 1 + cos (4 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \frac{1}{2} (\int 1 d x + \int cos (4 x) d x)

\int 1 d x = x

\int cos (4 x) d x = \frac{1}{4} sin (4 x)

= - \frac{1}{2} (x + \frac{1}{4} sin (4 x))

Add a constant to the solution

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

y^{^{'}} + t^{2} = 0

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

\frac{d y}{d x} = - \frac{y ^{2}}{1 + y ^{2}} e^{- x}

\frac{d}{d t} (3 - t)

x \to 1 + lim (1 - x^{2})

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