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

The integral of x-x^{1/2} is (x^2)/2-2/3 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 x-x^{1/2}

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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