What is the integral of 3-2(x)^{-1} ?

The integral of 3-2(x)^{-1} is 3x-2ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 3-2(x)^{-1}

integral

3 - 2 (x)^{- 1}

3 x - 2 ln ∣ x ∣ + C

Solution steps

\int 3 - 2 x^{- 1} d x

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

= \int 3 - \frac{2}{x} 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 3 d x - \int \frac{2}{x} d x

\int 3 d x = 3 x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= 3 x - 2 ln ∣ x ∣

Add a constant to the solution

= 3 x - 2 ln ∣ x ∣ + C

What is the integral of 3-2(x)^{-1} ?
The integral of 3-2(x)^{-1} is 3x-2ln|x|+C