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

The integral of 2/(x^2-x) is 2(-ln|x|+ln|x-1|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2/(x^2-x)

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

2 (- ln ∣ x ∣ + ln ∣ x - 1 ∣) + C

Solution steps

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

Take the constant out:

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

= 2 \cdot \int \frac{1}{x ^{2} - x} d x

Take the partial fraction of

\frac{1}{x ^{2} - x} : - \frac{1}{x} + \frac{1}{x - 1}

= 2 \cdot \int - \frac{1}{x} + \frac{1}{x - 1} d x

Apply the Sum Rule:

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

= 2 (- \int \frac{1}{x} d x + \int \frac{1}{x - 1} d x)

\int \frac{1}{x} d x = ln ∣ x ∣

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

= 2 (- ln ∣ x ∣ + ln ∣ x - 1 ∣)

Add a constant to the solution

= 2 (- ln ∣ x ∣ + ln ∣ x - 1 ∣) + C

\frac{d v}{d t}

(x + y)^{2} d x + (2 x y + x^{2} - 3) d y = 0

\frac{\partial}{\partial x} ((e^{x})^{2})

x \to c lim (- 6 + 3 (\frac{1}{3}))

\int x^{3} x^{2} - 6 d x

What is the integral of 2/(x^2-x) ?
The integral of 2/(x^2-x) is 2(-ln|x|+ln|x-1|)+C