What is the integral of x^{1/2}+4 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^{1/2}+4

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

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

Solution steps

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

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

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