What is the integral of (2/(5x)) ?

The integral of (2/(5x)) is 2/5 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 (2/(5x))

\int (\frac{2}{5 x}) d x

\frac{2}{5} ln ∣ x ∣ + C

Solution steps

\int \frac{2}{5 x} d x

Take the constant out:

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

= \frac{2}{5} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{2}{5} ln ∣ x ∣

Add a constant to the solution

= \frac{2}{5} ln ∣ x ∣ + C

(e^{7 e^{x}})^{^{'}}

\frac{16}{1 + x ^{4}}, 8 x^{2}

\int_{2}^{8} \frac{x}{x ^{2} + 6 x + 13} d x

f (x) = \frac{1}{4 x ^{2}}

\int x^{3} y^{2} d y