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

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

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

6 ln ∣ x ∣ + 2 x + x + C

Solution steps

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

Expand

\frac{6 + x + x}{x} : \frac{6}{x} + \frac{1}{x} + 1

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

\int \frac{6}{x} d x = 6 ln ∣ x ∣

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

\int 1 d x = x

= 6 ln ∣ x ∣ + 2 x + x

Add a constant to the solution

= 6 ln ∣ x ∣ + 2 x + x + C

\int_{1}^{2} (2 - x) d x

\int sin (π x) - cos (π x) d x

y^{\frac{1}{2}} (\frac{d y}{d x}) + y^{\frac{3}{2}} = 1

\frac{x ^{2} + 2 x - 5}{( x + 1 ) ^{2}}

f (x) = x - sin (x)

What is the integral of (6+sqrt(x)+x)/x ?
The integral of (6+sqrt(x)+x)/x is 6ln|x|+2sqrt(x)+x+C