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+1))/x

Solution

integral

\frac{( x + 1 )}{x}

Solution

x + ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

\int 1 d x = x

\int \frac{1}{x} d x = ln ∣ x ∣

= x + ln ∣ x ∣

Add a constant to the solution

= x + ln ∣ x ∣ + C

Graph

Popular Examples

integral of sec^5(x)

integral of ((x-y))/((x+y)^3)

integral of (x^2)/((x^2+4))

integral of e^x*x^{-2}

integral of x(ln(x))^2

Frequently Asked Questions (FAQ)

What is the integral of ((x+1))/x ?
The integral of ((x+1))/x is x+ln|x|+C