What is the integral of (x-1)/(x-5) ?

The integral of (x-1)/(x-5) is x-5+4ln|x-5|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x-1)/(x-5)

\int \frac{x - 1}{x - 5} d x

x - 5 + 4 ln ∣ x - 5 ∣ + C

Solution steps

\int \frac{x - 1}{x - 5} d x

Expand

\frac{x - 1}{x - 5} : \frac{x}{x - 5} - \frac{1}{x - 5}

Apply the Sum Rule:

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

= \int \frac{x}{x - 5} d x - \int \frac{1}{x - 5} d x

\int \frac{x}{x - 5} d x = x - 5 + 5 ln ∣ x - 5 ∣

\int \frac{1}{x - 5} d x = ln ∣ x - 5 ∣

= x - 5 + 5 ln ∣ x - 5 ∣ - ln ∣ x - 5 ∣

Simplify

= x - 5 + 4 ln ∣ x - 5 ∣

Add a constant to the solution

= x - 5 + 4 ln ∣ x - 5 ∣ + C

\int 3 x^{2} + 4 x + 5 d x

\int \frac{1}{1 + \frac{x}{2 L}} d x

\int x^{2} e^{2 x^{3} + 1} d x

\int (x + 5) 2 - x d x

\int 2 x - 2 x^{3} d x

What is the integral of (x-1)/(x-5) ?
The integral of (x-1)/(x-5) is x-5+4ln|x-5|+C