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

Popular >

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

\int 21 x^{2} + 2 d x

\int (2 - 4 t - 6 t^{3}) d t

\int 5 x \cdot cos (x) d x

\int (x ln (x) + \frac{1}{x ( x ^{2} + 1 )}) d x

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