What is the integral of 1/(9x) ?

The integral of 1/(9x) is 1/9 ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(9x)

\int \frac{1}{9 x} d x

\frac{1}{9} ln ∣ x ∣ + C

Solution steps

\int \frac{1}{9 x} d x

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{9} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{9} ln ∣ x ∣ + C

a re a 7 e^{x}, 7 x e^{x^{2}}, 1, 7 e

t an g e n t f (x) = \frac{x}{( 1 + x ^{2} )}, at x = 2

d er i v a t i v e f (x) = (3 x^{2} + 2) (8 x^{3} - 3)

\frac{d y}{d x} = 5 y x

\int \frac{30}{( x + 1 ) ( x ^{2} + 9 ) ^{2}} d x