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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

2 a^{2} ln ∣ x ∣ + C

Solution steps

\int x \frac{2 a ^{2}}{x ^{2}} d x

Take the constant out:

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

= 2 a^{2} \cdot \int x \frac{1}{x ^{2}} d x

Simplify

x \frac{1}{x ^{2}} : \frac{1}{x}

= 2 a^{2} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 a^{2} ln ∣ x ∣

Add a constant to the solution

= 2 a^{2} ln ∣ x ∣ + C

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