What is the integral of x^2+x^{-2} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^2+x^{-2}

\int x^{2} + x^{- 2} d x

\frac{x ^{3}}{3} - \frac{1}{x} + C

Solution steps

\int x^{2} + 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 x^{2} d x + \int x^{- 2} d x

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

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

= \frac{x ^{3}}{3} - \frac{1}{x}

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{1}{x} + C

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