en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of x/(x-12)

Solution

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

Solution

x - 12 + 12 ln ∣ x - 12 ∣ + C

Solution steps

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

Apply u-substitution

= \int \frac{u + 12}{u} d u

Expand

\frac{u + 12}{u} : 1 + \frac{12}{u}

= \int 1 + \frac{12}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d u + \int \frac{12}{u} d u

\int 1 d u = u

\int \frac{12}{u} d u = 12 ln ∣ u ∣

= u + 12 ln ∣ u ∣

Substitute back

u = x - 12

= x - 12 + 12 ln ∣ x - 12 ∣

Add a constant to the solution

= x - 12 + 12 ln ∣ x - 12 ∣ + C

Graph

Popular Examples

integral of x^3(x^2+1)^{1/2}

integral of x^2sin(3x^3)

integral of e^{5x-8}

integral of ((x+2))/(x^2+2x-3)

integral of (tan(x))^7

Frequently Asked Questions (FAQ)

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