What is the integral of (x+2)/(x+5) ?

The integral of (x+2)/(x+5) is -3ln|x+5|+x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+2)/(x+5)

\int \frac{x + 2}{x + 5} d x

- 3 ln ∣ x + 5 ∣ + x + C

Solution steps

\int \frac{x + 2}{x + 5} d x

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

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

\int \frac{3}{x + 5} d x = 3 ln ∣ x + 5 ∣

\int 1 d x = x

= - 3 ln ∣ x + 5 ∣ + x

Add a constant to the solution

= - 3 ln ∣ x + 5 ∣ + x + C

f (t) = t^{6}

f (x) = 5 x^{4} - 5 x^{2} + 7

\int \frac{1}{x ^{2} + 8 x + 16} d x

\frac{d}{d x} (lo g_{5} (e^{x}))

\int x^{2} sin (10 x) d x

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