What is the integral of cos^2(2ax) ?

The integral of cos^2(2ax) is x-x/2+1/(8a)sin(4ax)+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(2ax)

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

x - \frac{x}{2} + \frac{1}{8 a} sin (4 a x) + C

Solution steps

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

Rewrite using trig identities

= \int 1 - sin^{2} (2 a 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

= \int 1 d x - \int sin^{2} (2 a x) d x

\int 1 d x = x

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

= x - (\frac{x}{2} - \frac{1}{8 a} sin (4 a x))

Simplify

= x - \frac{x}{2} + \frac{1}{8 a} sin (4 a x)

Add a constant to the solution

= x - \frac{x}{2} + \frac{1}{8 a} sin (4 a x) + C

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

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

x^{2} - 10, 9 x

\int \frac{1}{e ^{2 x} - 4} d x

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

What is the integral of cos^2(2ax) ?
The integral of cos^2(2ax) is x-x/2+1/(8a)sin(4ax)+C