What is the integral of 3/(12x-1) ?

The integral of 3/(12x-1) is 1/4 ln|12x-1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3/(12x-1)

\int \frac{3}{12 x - 1} d x

\frac{1}{4} ln ∣ 12 x - 1 ∣ + C

Solution steps

\int \frac{3}{12 x - 1} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{12 x - 1} d x

Apply u-substitution

: \int \frac{1}{12 u} d u

= 3 \cdot \int \frac{1}{12 u} d u

Take the constant out:

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

= 3 \cdot \frac{1}{12} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 \cdot \frac{1}{12} ln ∣ u ∣

Substitute back

u = 12 x - 1

= 3 \cdot \frac{1}{12} ln ∣ 12 x - 1 ∣

Simplify

3 \cdot \frac{1}{12} ln ∣ 12 x - 1 ∣ : \frac{1}{4} ln ∣ 12 x - 1 ∣

= \frac{1}{4} ln ∣ 12 x - 1 ∣

Add a constant to the solution

= \frac{1}{4} ln ∣ 12 x - 1 ∣ + C

f (x) = \frac{x}{e ^{x}}

\frac{\partial}{\partial x} (x^{2} - x y + 8 y^{2})

\int_{0}^{1} 5 e^{- 2 x} d x

x^{3} - 4 x^{2} - 7 x + 8

\frac{d}{d x} (\frac{6 x}{x + 1})

What is the integral of 3/(12x-1) ?
The integral of 3/(12x-1) is 1/4 ln|12x-1|+C