What is the integral of 5/(3x) ?

The integral of 5/(3x) is 5/3 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 5/(3x)

\int \frac{5}{3 x} d x

\frac{5}{3} ln ∣ x ∣ + C

Solution steps

\int \frac{5}{3 x} d x

Take the constant out:

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

= \frac{5}{3} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{5}{3} ln ∣ x ∣

Add a constant to the solution

= \frac{5}{3} ln ∣ x ∣ + C

\int \frac{8}{x ^{2} - 16} d x

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

\int 7 (2 x - 9)^{6} d x

\int x^{2} (2 x^{3} - 5)^{6} d x

\int x^{3} (8 x + x) d x