What is the integral of 3/(9x) ?

The integral of 3/(9x) is 1/3 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 3/(9x)

\int \frac{3}{9 x} d x

\frac{1}{3} ln ∣ x ∣ + C

Solution steps

\int \frac{3}{9 x} d x

Take the constant out:

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

= \frac{3}{9} \cdot \int \frac{1}{x} d x

Cancel the common factor:

3

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{3} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{3} ln ∣ x ∣ + C

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

\int \frac{( x ^{2} arctan ( x ) )}{( 1 + x ^{2} )} d x

\int - x^{3} ln (x) d x

\int sin^{2} (x) e^{- x} d x

\int ln^{- 1} (x) d x