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

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

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

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

Solution steps

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

Rewrite using trig identities

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

\int 1 d x = x

\int cos (x) d x = sin (x)

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

Add a constant to the solution

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

x \to 3 lim (2 x^{2} - 7 x + 6)

\frac{d}{d x} (\frac{n}{x + 1})

\int \frac{1}{x \cdot 1 - x} d x

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

sin (x), \frac{π}{4}

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