en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

x^{2} - \frac{2}{x} + C

Solution steps

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

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

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

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

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

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

Add a constant to the solution

= x^{2} - \frac{2}{x} + C

Popular Examples

integral of x/(6+pi)

\int \frac{x}{6 + π} d x

derivative of (x^2*ln(x))

\frac{d}{d x} ((x^{2}) \cdot ln (x))

derivative of f(x)=(x^2)/(9+2x)derivative of

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

integral from 0 to 1 of pi(x-x^{10})

\int_{0}^{1} π (x - x^{10}) d x

derivative of 3x^2e^x+x^3e^x

\frac{d}{d x} (3 x^{2} e^{x} + x^{3} e^{x})

Frequently Asked Questions (FAQ)

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