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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (8+sqrt(x)+x)/x

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

8 ln ∣ x ∣ + 2 x + x + C

Solution steps

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

Expand

\frac{8 + x + x}{x} : \frac{8}{x} + \frac{1}{x} + 1

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

\int \frac{8}{x} d x = 8 ln ∣ x ∣

\int \frac{1}{x} d x = 2 x

\int 1 d x = x

= 8 ln ∣ x ∣ + 2 x + x

Add a constant to the solution

= 8 ln ∣ x ∣ + 2 x + x + C

\frac{d x}{d t} = x sin (t)

x \to 1 - lim (arcsin (x))

\int x^{2} x^{3} + 4 d x

y^{^{'}} - 4 y = 6 e^{6 t}

\frac{d}{d x} ((c_{1} + c_{2} x) e^{- 3 x})

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