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

Popular >

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

\frac{9}{t ^{3}}

\frac{d}{d x} (x^{2} + 6 x)

f (x) = \frac{x ^{\frac{1}{2}}}{x + 9}, at x = 1

x d y - y d x + y^{2} d x = 0

\frac{d}{d x} (4 sinh (2 x))

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