What is the integral of (14x+6)/(x^2-x-2) ?

The integral of (14x+6)/(x^2-x-2) is 8/3 ln|x+1|+34/3 ln|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 (14x+6)/(x^2-x-2)

\int \frac{14 x + 6}{x ^{2} - x - 2} d x

\frac{8}{3} ln ∣ x + 1 ∣ + \frac{34}{3} ln ∣ x - 2 ∣ + C

Solution steps

\int \frac{14 x + 6}{x ^{2} - x - 2} d x

Take the partial fraction of

\frac{14 x + 6}{x ^{2} - x - 2} : \frac{8}{3 ( x + 1 )} + \frac{34}{3 ( x - 2 )}

= \int \frac{8}{3 ( x + 1 )} + \frac{34}{3 ( 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 \frac{8}{3 ( x + 1 )} d x + \int \frac{34}{3 ( x - 2 )} d x

\int \frac{8}{3 ( x + 1 )} d x = \frac{8}{3} ln ∣ x + 1 ∣

\int \frac{34}{3 ( x - 2 )} d x = \frac{34}{3} ln ∣ x - 2 ∣

= \frac{8}{3} ln ∣ x + 1 ∣ + \frac{34}{3} ln ∣ x - 2 ∣

Add a constant to the solution

= \frac{8}{3} ln ∣ x + 1 ∣ + \frac{34}{3} ln ∣ x - 2 ∣ + C

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

\int (x^{3} + 2 x + 14) sin (3 x) d x

\int \frac{x ^{2}}{x ( x ^{2} - 9 )} d x

\int (sin (x) + 3 cos (x))^{2} d x

\int sin^{6} (x) cos^{7} (x) d x

What is the integral of (14x+6)/(x^2-x-2) ?
The integral of (14x+6)/(x^2-x-2) is 8/3 ln|x+1|+34/3 ln|x-2|+C