What is the integral of (x+5)/(x+6) ?

The integral of (x+5)/(x+6) is -ln|x+6|+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+5)/(x+6)

\int \frac{x + 5}{x + 6} d x

- ln ∣ x + 6 ∣ + x + C

Solution steps

\int \frac{x + 5}{x + 6} d x

\frac{x + 5}{x + 6} = - \frac{1}{x + 6} + 1

= \int - \frac{1}{x + 6} + 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{1}{x + 6} d x + \int 1 d x

\int \frac{1}{x + 6} d x = ln ∣ x + 6 ∣

\int 1 d x = x

= - ln ∣ x + 6 ∣ + x

Add a constant to the solution

= - ln ∣ x + 6 ∣ + x + C

\frac{d}{d x} (cos (x) - sin (x))

\frac{d y}{d x} = x^{9} + 1

t^{2} \frac{d y}{d t} + 4 t y - y^{3} = 0, y (1) = \frac{3}{2}

y = \frac{3}{sin ( x ) + cos ( x )}

\int \frac{48}{36 - x ^{2}} d x

What is the integral of (x+5)/(x+6) ?
The integral of (x+5)/(x+6) is -ln|x+6|+x+C