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

The integral of ((3+sqrt(x)+x))/x is 3ln|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 ((3+sqrt(x)+x))/x

\int \frac{( 3 + x + x )}{x} d x

3 ln ∣ x ∣ + 2 x + x + C

Solution steps

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

Expand

\frac{3 + x + x}{x} : \frac{3}{x} + \frac{1}{x} + 1

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

\int 1 d x = x

= 3 ln ∣ x ∣ + 2 x + x

Add a constant to the solution

= 3 ln ∣ x ∣ + 2 x + x + C

\int x (x + 9)^{5} d x

\int \frac{1}{x ( 2 x - 1 )} d x

\int \frac{x \cdot arctan ( x )}{( 1 + x ^{2} ) ^{3}} d x

\int 3 x (x^{2} + 6)^{5} d x

\int tan (12 x) d x

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