What is the integral of ((20x+9))/(x^2-2x-15) ?

The integral of ((20x+9))/(x^2-2x-15) is 51/8 ln|x+3|+109/8 ln|x-5|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((20x+9))/(x^2-2x-15)

\int \frac{( 20 x + 9 )}{x ^{2} - 2 x - 15} d x

\frac{51}{8} ln ∣ x + 3 ∣ + \frac{109}{8} ln ∣ x - 5 ∣ + C

Solution steps

\int \frac{20 x + 9}{x ^{2} - 2 x - 15} d x

Take the partial fraction of

\frac{20 x + 9}{x ^{2} - 2 x - 15} : \frac{51}{8 ( x + 3 )} + \frac{109}{8 ( x - 5 )}

= \int \frac{51}{8 ( x + 3 )} + \frac{109}{8 ( x - 5 )} 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{51}{8 ( x + 3 )} d x + \int \frac{109}{8 ( x - 5 )} d x

\int \frac{51}{8 ( x + 3 )} d x = \frac{51}{8} ln ∣ x + 3 ∣

\int \frac{109}{8 ( x - 5 )} d x = \frac{109}{8} ln ∣ x - 5 ∣

= \frac{51}{8} ln ∣ x + 3 ∣ + \frac{109}{8} ln ∣ x - 5 ∣

Add a constant to the solution

= \frac{51}{8} ln ∣ x + 3 ∣ + \frac{109}{8} ln ∣ x - 5 ∣ + C

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

\int x (1 + x) d x

\int \frac{8}{9} csc^{2} (\frac{x}{9}) d x

\int (12 x^{2} + 6 x - 5) d x

\int \frac{5 x - 3}{x ^{2} + 7 x + 6} d x

What is the integral of ((20x+9))/(x^2-2x-15) ?
The integral of ((20x+9))/(x^2-2x-15) is 51/8 ln|x+3|+109/8 ln|x-5|+C