What is the integral of (6x-12)/(x^2) ?

The integral of (6x-12)/(x^2) is 6ln|x|+(12)/x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (6x-12)/(x^2)

\int \frac{6 x - 12}{x ^{2}} d x

6 ln ∣ x ∣ + \frac{12}{x} + C

Solution steps

\int \frac{6 x - 12}{x ^{2}} d x

Expand

\frac{6 x - 12}{x ^{2}} : \frac{6}{x} - \frac{12}{x ^{2}}

= \int \frac{6}{x} - \frac{12}{x ^{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{6}{x} d x - \int \frac{12}{x ^{2}} d x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

\int \frac{12}{x ^{2}} d x = - \frac{12}{x}

= 6 ln ∣ x ∣ - (- \frac{12}{x})

Simplify

= 6 ln ∣ x ∣ + \frac{12}{x}

Add a constant to the solution

= 6 ln ∣ x ∣ + \frac{12}{x} + C

What is the integral of (6x-12)/(x^2) ?
The integral of (6x-12)/(x^2) is 6ln|x|+(12)/x+C