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

The integral of ((x^2+3))/(x^2-3x+2) is x-4ln|x-1|+7ln|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+3))/(x^2-3x+2)

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

x - 4 ln ∣ x - 1 ∣ + 7 ln ∣ x - 2 ∣ + C

Solution steps

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

Take the partial fraction of

\frac{x ^{2} + 3}{x ^{2} - 3 x + 2} : 1 - \frac{4}{x - 1} + \frac{7}{x - 2}

= \int 1 - \frac{4}{x - 1} + \frac{7}{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{4}{x - 1} d x + \int \frac{7}{x - 2} d x

\int 1 d x = x

\int \frac{4}{x - 1} d x = 4 ln ∣ x - 1 ∣

\int \frac{7}{x - 2} d x = 7 ln ∣ x - 2 ∣

= x - 4 ln ∣ x - 1 ∣ + 7 ln ∣ x - 2 ∣

Add a constant to the solution

= x - 4 ln ∣ x - 1 ∣ + 7 ln ∣ x - 2 ∣ + C

\int x (3 x - 2) d x

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

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

y = 4 x^{3} - 2 x

x \to 5 lim (x (5))

What is the integral of ((x^2+3))/(x^2-3x+2) ?
The integral of ((x^2+3))/(x^2-3x+2) is x-4ln|x-1|+7ln|x-2|+C