What is the integral of (x-2)/(x^2-4x+4) ?

The integral of (x-2)/(x^2-4x+4) is -x/(x-2)+ln|x-2|+2/(x-2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x-2)/(x^2-4x+4)

\int \frac{x - 2}{x ^{2} - 4 x + 4} d x

- \frac{x}{x - 2} + ln ∣ x - 2 ∣ + \frac{2}{x - 2} + C

Solution steps

\int \frac{x - 2}{x ^{2} - 4 x + 4} d x

Expand

\frac{x - 2}{x ^{2} - 4 x + 4} : \frac{x}{x ^{2} - 4 x + 4} - \frac{2}{x ^{2} - 4 x + 4}

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 ^{2} - 4 x + 4} d x - \int \frac{2}{x ^{2} - 4 x + 4} d x

\int \frac{x}{x ^{2} - 4 x + 4} d x = - \frac{x}{x - 2} + ln ∣ x - 2 ∣

\int \frac{2}{x ^{2} - 4 x + 4} d x = - \frac{2}{x - 2}

= - \frac{x}{x - 2} + ln ∣ x - 2 ∣ - (- \frac{2}{x - 2})

Simplify

= - \frac{x}{x - 2} + ln ∣ x - 2 ∣ + \frac{2}{x - 2}

Add a constant to the solution

= - \frac{x}{x - 2} + ln ∣ x - 2 ∣ + \frac{2}{x - 2} + C

\int \frac{sin ( x )}{tan ^{2} ( x )} d x

\int e^{y} (y - 1) d y

\int x^{3} e^{\frac{x}{3}} d x

\int \frac{x}{( 1 + x ^{2} ) ^{4}} d x

\int \frac{3 x - 1}{1 - 2 x} d x

What is the integral of (x-2)/(x^2-4x+4) ?
The integral of (x-2)/(x^2-4x+4) is -x/(x-2)+ln|x-2|+2/(x-2)+C