en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 1+1/(2x)

Solution

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

Solution

x + \frac{1}{2} ln ∣ x ∣ + C

Solution steps

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

\int 1 d x = x

\int \frac{1}{2 x} d x = \frac{1}{2} ln ∣ x ∣

= x + \frac{1}{2} ln ∣ x ∣

Add a constant to the solution

= x + \frac{1}{2} ln ∣ x ∣ + C

Graph

Popular Examples

integral from 1 to 3 of e^x

integral from 3 to 6 of x/(x^2+6x+13)

(\partial)/(\partial y)(2x^{4y})

limit as x approaches-0 of f(x)

Frequently Asked Questions (FAQ)

What is the integral of 1+1/(2x) ?
The integral of 1+1/(2x) is x+1/2 ln|x|+C