What is the integral of (x^2)/(x^2-3x+2) ?

The integral of (x^2)/(x^2-3x+2) is x-ln|x-1|+4ln|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^2-3x+2)

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

x - ln ∣ x - 1 ∣ + 4 ln ∣ x - 2 ∣ + C

Solution steps

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

Take the partial fraction of

\frac{x ^{2}}{x ^{2} - 3 x + 2} : 1 - \frac{1}{x - 1} + \frac{4}{x - 2}

= \int 1 - \frac{1}{x - 1} + \frac{4}{x - 2} 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

= \int 1 d x - \int \frac{1}{x - 1} d x + \int \frac{4}{x - 2} d x

\int 1 d x = x

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

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

= x - ln ∣ x - 1 ∣ + 4 ln ∣ x - 2 ∣

Add a constant to the solution

= x - ln ∣ x - 1 ∣ + 4 ln ∣ x - 2 ∣ + C

x \to 4 lim (\frac{1}{x ^{2} - 16})

2 t^{3}

\frac{\partial}{\partial x} (\frac{1}{x ^{2}} - \frac{1}{1 - x - y})

2 x^{2} - 3

e^{- s}

What is the integral of (x^2)/(x^2-3x+2) ?
The integral of (x^2)/(x^2-3x+2) is x-ln|x-1|+4ln|x-2|+C