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

Simplify

= (- \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 ∣

Simplify

= - \frac{1}{2} ln ∣ x ∣

Add a constant to the solution

= - \frac{1}{2} ln ∣ x ∣ + C

\int \frac{x ^{2} + 2 x + 4}{x ^{2} - 4} d x

\int x^{2} (sin (2) x^{3} + 4 x) d x

\int e^{x} + 3 sin (x) d x

\int \frac{( ln ( x ) ) ^{p}}{x} d x

\int \frac{9 sin ( x )}{x} d x