What is the integral of 3csc^2(2x) ?

The integral of 3csc^2(2x) is -3/2 cot(2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3csc^2(2x)

\int 3 csc^{2} (2 x) d x

- \frac{3}{2} cot (2 x) + C

Solution steps

\int 3 csc^{2} (2 x) d x

Take the constant out:

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

= 3 \cdot \int csc^{2} (2 x) d x

Apply u-substitution

: \int csc^{2} (u) \frac{1}{2} d u

= 3 \cdot \int csc^{2} (u) \frac{1}{2} d u

Take the constant out:

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

= 3 \cdot \frac{1}{2} \cdot \int csc^{2} (u) d u

Use the common integral:

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

= 3 \cdot \frac{1}{2} (- cot (u))

Substitute back

u = 2 x

= 3 \cdot \frac{1}{2} (- cot (2 x))

Simplify

3 \cdot \frac{1}{2} (- cot (2 x)) : - \frac{3}{2} cot (2 x)

= - \frac{3}{2} cot (2 x)

Add a constant to the solution

= - \frac{3}{2} cot (2 x) + C

\int 9 x - 7 d x

\int 3^{- 2 x + 1} d x

\int \frac{5}{16 - 9 x ^{2}} d x

\frac{2}{3 x ^{2}}

\int \frac{ln ( x )}{x ( 1 + ln ( x ) )} d x

What is the integral of 3csc^2(2x) ?
The integral of 3csc^2(2x) is -3/2 cot(2x)+C