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+2/x

Solution

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

Solution

\frac{x ^{2}}{2} + 2 ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{x ^{2}}{2} + 2 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} + 2 ln ∣ x ∣ + C

Graph

Popular Examples

integral of 3e^x+4

integral of (2x+1)*cos(4x)

integral of (5x^2+14x+10)/((x+2)(x+1)^2)

integral of sin(αx)

integral of (5x-4)/(x^2+3x+2)

Frequently Asked Questions (FAQ)

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