en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cot(x/2)

Solution

\int cot (\frac{x}{2}) d x

Solution

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

Solution steps

\int cot (\frac{x}{2}) d x

Rewrite using trig identities

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

Apply u-substitution

: \int \frac{2}{u} d u

= \int \frac{2}{u} d u

Take the constant out:

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

= 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 ln ∣ u ∣

Substitute back

u = sin (\frac{x}{2})

= 2 ln sin (\frac{x}{2})

Add a constant to the solution

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

Popular Examples

derivative of f(-2)=3x-7 derivative of

f (- 2) = 3 x - 7

derivative of f(x)=sin(pix)derivative of

f (x) = sin (π x)

d/(dy)(xsin(y)+ycos(x))

\frac{d}{d y} (x sin (y) + y cos (x))

integral from 0 to 1 of x^3

\int_{0}^{1} x^{3} d x

derivative of 3/(x(x^2-4))

\frac{d}{d x} (\frac{3}{x ( x ^{2} - 4 )})

Frequently Asked Questions (FAQ)

What is the integral of cot(x/2) ?
The integral of cot(x/2) is 2ln|sin(x/2)|+C