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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{1}{3} x^{\frac{3}{2}} + 4 x + C

Solution steps

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

\int \frac{x}{2} d x = \frac{1}{3} x^{\frac{3}{2}}

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

= \frac{1}{3} x^{\frac{3}{2}} + 4 x

Add a constant to the solution

= \frac{1}{3} x^{\frac{3}{2}} + 4 x + C

\frac{\partial}{\partial x} (\frac{x + y}{x y - 1})

\frac{d y}{d x} = sin (y) + 1

\frac{d}{d x} (x^{3 c o s (x)})

f (x) = 7 x

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