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

The integral of 2/(xln(x^2)) is ln(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 2/(xln(x^2))

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

ln (2 ∣ ln (x) ∣) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= 2 \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

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 2 \cdot \frac{1}{2} ln ∣ v ∣

Substitute back

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

Simplify

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

= ln (2 ∣ ln (x) ∣)

Add a constant to the solution

= ln (2 ∣ ln (x) ∣) + C

\int x^{2} \frac{1}{1 - x ^{2}} d x

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

\int sin (5 x + π) d x

\int x^{2} e^{\frac{x}{4}} d x

\int \frac{1}{x ^{2}} \cdot 1 + \frac{1}{x} d x

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