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

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

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

- 2 cot (2 x) + C

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Apply u-substitution

: \int 2 csc^{2} (v) d v

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

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

Simplify

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

= - 2 cot (2 x)

Add a constant to the solution

= - 2 cot (2 x) + C

\int \frac{2 x + 1}{3 x + 2} d x

\int x^{3} e^{- a x} d x

\int (3 x - 1)^{2003} d x

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

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