What is the integral of (x+34)/(x^2-4x-12) ?

The integral of (x+34)/(x^2-4x-12) is -4ln|x+2|+5ln|x-6|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+34)/(x^2-4x-12)

\int \frac{x + 34}{x ^{2} - 4 x - 12} d x

- 4 ln ∣ x + 2 ∣ + 5 ln ∣ x - 6 ∣ + C

Solution steps

\int \frac{x + 34}{x ^{2} - 4 x - 12} d x

Take the partial fraction of

\frac{x + 34}{x ^{2} - 4 x - 12} : - \frac{4}{x + 2} + \frac{5}{x - 6}

= \int - \frac{4}{x + 2} + \frac{5}{x - 6} 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{4}{x + 2} d x + \int \frac{5}{x - 6} d x

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

\int \frac{5}{x - 6} d x = 5 ln ∣ x - 6 ∣

= - 4 ln ∣ x + 2 ∣ + 5 ln ∣ x - 6 ∣

Add a constant to the solution

= - 4 ln ∣ x + 2 ∣ + 5 ln ∣ x - 6 ∣ + C

\int x^{5} - π^{5} + x^{2} - π^{2} d x

\int (a x^{6} + b x^{4} + 3 c) d x

\int csc (x) sin (x) d x

\int tan (x^{2}) x d x

\int e^{x} - e d x

What is the integral of (x+34)/(x^2-4x-12) ?
The integral of (x+34)/(x^2-4x-12) is -4ln|x+2|+5ln|x-6|+C