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

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

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

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

Solution steps

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

Rewrite using trig identities

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

\int 1 d x = x

\int cos (2 x) d x = \frac{1}{2} sin (2 x)

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

Add a constant to the solution

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

\int (2^{x}) d x

x \to 7 - lim (4 x)

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

x + 2, x, - 2, 2

\frac{d}{d x} (\frac{ln ( x )}{1 - x})

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