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

The integral of (sqrt(x)+x)/(sqrt(x)) is x+2/3 x^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

x + \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

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

Expand

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

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

\int \frac{x}{x} d x = \frac{2}{3} x^{\frac{3}{2}}

= x + \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= x + \frac{2}{3} x^{\frac{3}{2}} + C

What is the integral of (sqrt(x)+x)/(sqrt(x)) ?
The integral of (sqrt(x)+x)/(sqrt(x)) is x+2/3 x^{3/2}+C