What is the integral of 8/(x+1)+x ?

The integral of 8/(x+1)+x is 8ln|x+1|+(x^2)/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 8/(x+1)+x

\int \frac{8}{x + 1} + x d x

8 ln ∣ x + 1 ∣ + \frac{x ^{2}}{2} + C

Solution steps

\int \frac{8}{x + 1} + x 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{8}{x + 1} d x + \int x d x

\int \frac{8}{x + 1} d x = 8 ln ∣ x + 1 ∣

\int x d x = \frac{x ^{2}}{2}

= 8 ln ∣ x + 1 ∣ + \frac{x ^{2}}{2}

Add a constant to the solution

= 8 ln ∣ x + 1 ∣ + \frac{x ^{2}}{2} + C

What is the integral of 8/(x+1)+x ?
The integral of 8/(x+1)+x is 8ln|x+1|+(x^2)/2+C