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

The integral of (x^3)/(x^2-3x+2) is (x^2)/2+3x-ln|x-1|+8ln|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^3)/(x^2-3x+2)

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

\frac{x ^{2}}{2} + 3 x - ln ∣ x - 1 ∣ + 8 ln ∣ x - 2 ∣ + C

Solution steps

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

Take the partial fraction of

\frac{x ^{3}}{x ^{2} - 3 x + 2} : x + 3 - \frac{1}{x - 1} + \frac{8}{x - 2}

= \int x + 3 - \frac{1}{x - 1} + \frac{8}{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 x d x + \int 3 d x - \int \frac{1}{x - 1} d x + \int \frac{8}{x - 2} d x

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

\int 3 d x = 3 x

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

\int \frac{8}{x - 2} d x = 8 ln ∣ x - 2 ∣

= \frac{x ^{2}}{2} + 3 x - ln ∣ x - 1 ∣ + 8 ln ∣ x - 2 ∣

Add a constant to the solution

= \frac{x ^{2}}{2} + 3 x - ln ∣ x - 1 ∣ + 8 ln ∣ x - 2 ∣ + C

\int (x^{5} + \frac{1}{x ^{3}} + 4) d x

\int - 3 x^{4} e^{x^{5}} d x

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

\int \frac{x}{( x ^{2} + 4 ) ^{15}} d x

\int arccos (\frac{x}{2}) d x

What is the integral of (x^3)/(x^2-3x+2) ?
The integral of (x^3)/(x^2-3x+2) is (x^2)/2+3x-ln|x-1|+8ln|x-2|+C