en

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

Solution

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

Solution

x + 2 ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{x + 2}{x} : 1 + \frac{2}{x}

= \int 1 + \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 1 d x + \int \frac{2}{x} d x

\int 1 d x = x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= x + 2 ln ∣ x ∣

Add a constant to the solution

= x + 2 ln ∣ x ∣ + C

Graph

Popular Examples

derivative of a^xln(x)

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

11x-4ysqrt(x^2+1)(dy)/(dx)=0

11 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0

derivative of f(t)=sqrt(4t^2-t)derivative of

f (t) = 4 t^{2} - t

limit as x approaches 1 of x^2-x

x \to 1 lim (x^{2} - x)

tangent of 9x^2-x^3 tangent of

9 x^{2} - x^{3}

Frequently Asked Questions (FAQ)

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