What is the integral of sqrt(x)-1/2 x+2/(sqrt(x)) ?

The integral of sqrt(x)-1/2 x+2/(sqrt(x)) is 2/3 x^{3/2}-(x^2)/4+4sqrt(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sqrt(x)-1/2 x+2/(sqrt(x))

\int x - \frac{1}{2} x + \frac{2}{x} d x

\frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{4} + 4 x + C

Solution steps

\int x - \frac{1}{2} x + \frac{2}{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 x d x - \int \frac{1}{2} x d x + \int \frac{2}{x} d x

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

\int \frac{1}{2} x d x = \frac{x ^{2}}{4}

\int \frac{2}{x} d x = 4 x

= \frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{4} + 4 x

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{4} + 4 x + C

What is the integral of sqrt(x)-1/2 x+2/(sqrt(x)) ?
The integral of sqrt(x)-1/2 x+2/(sqrt(x)) is 2/3 x^{3/2}-(x^2)/4+4sqrt(x)+C