What is the integral of (x-2)/(x+3) ?

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

\int \frac{x - 2}{x + 3} d x

- 5 ln ∣ x + 3 ∣ + x + C

Solution steps

\int \frac{x - 2}{x + 3} d x

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

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

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

\int 1 d x = x

= - 5 ln ∣ x + 3 ∣ + x

Add a constant to the solution

= - 5 ln ∣ x + 3 ∣ + x + C

\int cos (\frac{nπ x}{L}) d x

\frac{d}{d x} (2 (x)^{4})

\frac{d}{d x} (\frac{6 x ^{2} + 4}{3 y ^{2} - 4})

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

\frac{d}{d x} (3^{2 x^{2}} \cdot x)

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