What is the integral of (x+11)/(x^2-2x-15) ?

The integral of (x+11)/(x^2-2x-15) is -ln|x+3|+2ln|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 (x+11)/(x^2-2x-15)

\int \frac{x + 11}{x ^{2} - 2 x - 15} d x

- ln ∣ x + 3 ∣ + 2 ln ∣ x - 5 ∣ + C

Solution steps

\int \frac{x + 11}{x ^{2} - 2 x - 15} d x

Take the partial fraction of

\frac{x + 11}{x ^{2} - 2 x - 15} : - \frac{1}{x + 3} + \frac{2}{x - 5}

= \int - \frac{1}{x + 3} + \frac{2}{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{1}{x + 3} d x + \int \frac{2}{x - 5} d x

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

\int \frac{2}{x - 5} d x = 2 ln ∣ x - 5 ∣

= - ln ∣ x + 3 ∣ + 2 ln ∣ x - 5 ∣

Add a constant to the solution

= - ln ∣ x + 3 ∣ + 2 ln ∣ x - 5 ∣ + C

\int cos (10 θ) d θ

f (x) = x, at x = 81

\frac{ln ( 1 + x ^{2} )}{x}

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

\int x^{3} \cdot e^{- 2 x} d x

What is the integral of (x+11)/(x^2-2x-15) ?
The integral of (x+11)/(x^2-2x-15) is -ln|x+3|+2ln|x-5|+C