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

The integral of (csc^2(x/2)) is -2cot(x/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (csc^2(x/2))

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

- 2 cot (\frac{x}{2}) + C

Solution steps

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

Apply u-substitution

: \int csc^{2} (u) \cdot 2 d u

= \int csc^{2} (u) \cdot 2 d u

Take the constant out:

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

= 2 \cdot \int csc^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= 2 (- cot (u))

Substitute back

u = \frac{x}{2}

= 2 (- cot (\frac{x}{2}))

Simplify

= - 2 cot (\frac{x}{2})

Add a constant to the solution

= - 2 cot (\frac{x}{2}) + C

y = (t - 5) (t^{2} - 3), (2, - 3)

x \to 0 lim (x^{18} ln (x))

\frac{d}{d x} ((x^{3} - 1)^{100})

23 t

x^{^{''}} - 3 x^{^{'}} + 2 x = 0

What is the integral of (csc^2(x/2)) ?
The integral of (csc^2(x/2)) is -2cot(x/2)+C