en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2x-2/x

Solution

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

Solution

x^{2} - 2 ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= x^{2} - 2 ln ∣ x ∣

Add a constant to the solution

= x^{2} - 2 ln ∣ x ∣ + C

Graph

Popular Examples

(\partial)/(\partial y)(xarctan(y/z))

\frac{\partial}{\partial y} (x arctan (\frac{y}{z}))

limit as x approaches+(-3) of 2x+5

x \to + (- 3) lim (2 x + 5)

derivative of g(u)=sqrt(2)u+sqrt(3u)derivative of

g (u) = 2 u + 3 u

limit as x approaches 0 of-2x+1

x \to 0 lim (- 2 x + 1)

derivative of (a^x/(ln(a)))

\frac{d}{d x} (\frac{a ^{x}}{ln ( a )})

Frequently Asked Questions (FAQ)

What is the integral of 2x-2/x ?
The integral of 2x-2/x is x^2-2ln|x|+C