What is the integral of (1/(2x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1/(2x))

\int (\frac{1}{2 x}) d x

\frac{1}{2} ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{2} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ x ∣ + C

\frac{d}{d x} (\frac{2 x - 3}{2 x + 5})

\int (x - 3) \cdot cos (x) d x

\int \frac{5 r ^{2}}{r + 3} d r

\frac{d}{d x} (x^{2} ln (5 x))

(x - 2)^{2}