What is the integral of 1+1/x+1/(x^2) ?

The integral of 1+1/x+1/(x^2) is x+ln|x|-1/x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1+1/x+1/(x^2)

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

x + ln ∣ x ∣ - \frac{1}{x} + C

Solution steps

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

\int 1 d x = x

\int \frac{1}{x} d x = ln ∣ x ∣

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

= x + ln ∣ x ∣ - \frac{1}{x}

Add a constant to the solution

= x + ln ∣ x ∣ - \frac{1}{x} + C

What is the integral of 1+1/x+1/(x^2) ?
The integral of 1+1/x+1/(x^2) is x+ln|x|-1/x+C