What is the integral of 4/(xln(x^2)) ?

The integral of 4/(xln(x^2)) is 2ln(2|ln(x)|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4/(xln(x^2))

\int \frac{4}{x ln ( x ^{2} )} d x

2 ln (2 ∣ ln (x) ∣) + C

Solution steps

\int \frac{4}{x ln ( x ^{2} )} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{x ln ( x ^{2} )} d x

Apply u-substitution

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

= 4 \cdot \int \frac{1}{2 u ln ( u )} d u

Take the constant out:

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

= 4 \cdot \frac{1}{2} \cdot \int \frac{1}{u ln ( u )} d u

Apply u-substitution

: \int \frac{1}{v} d v

= 4 \cdot \frac{1}{2} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 4 \cdot \frac{1}{2} ln ∣ v ∣

Substitute back

= 4 \cdot \frac{1}{2} ln ln (x^{2})

Simplify

4 \cdot \frac{1}{2} ln ln (x^{2}) : 2 ln (2 ∣ ln (x) ∣)

= 2 ln (2 ∣ ln (x) ∣)

Add a constant to the solution

= 2 ln (2 ∣ ln (x) ∣) + C

\int e^{- 2 t} sin (h) (3 t) d t

\int (\frac{7}{9 - 16 x ^{2}}) d x

\int \frac{3}{300 + x} d x

\int \frac{3 w}{16 w ^{4} - 81} d w

\int \frac{x ^{4}}{x ^{2} + 25} d x

What is the integral of 4/(xln(x^2)) ?
The integral of 4/(xln(x^2)) is 2ln(2|ln(x)|)+C