en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of x+x^{-1}

Solution

\int x + x^{- 1} d x

Solution

\frac{x ^{2}}{2} + ln ∣ x ∣ + C

Solution steps

\int x + x^{- 1} 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 x d x + \int x^{- 1} d x

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

\int x^{- 1} d x = ln ∣ x ∣

= \frac{x ^{2}}{2} + ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} + ln ∣ x ∣ + C

Graph

Popular Examples

integral of (z^3)/(\sqrt[3]{6+z^4)}

integral of 2x^2(x-2)

integral of sin(\sqrt[4]{x-1})

integral of (2x^2+7x^{-2})

integral of ce^{-x/2}

Frequently Asked Questions (FAQ)

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