What is the integral of (sqrt(x)-x)^2 ?

The integral of (sqrt(x)-x)^2 is (x^2)/2-4/5 x^{5/2}+(x^3)/3+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)-x)^2

\int (x - x)^{2} d x

\frac{x ^{2}}{2} - \frac{4}{5} x^{\frac{5}{2}} + \frac{x ^{3}}{3} + C

Solution steps

\int (x - x)^{2} d x

Expand

(x - x)^{2} : x - 2 x^{\frac{3}{2}} + x^{2}

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

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

\int 2 x^{\frac{3}{2}} d x = \frac{4}{5} x^{\frac{5}{2}}

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

= \frac{x ^{2}}{2} - \frac{4}{5} x^{\frac{5}{2}} + \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{2}}{2} - \frac{4}{5} x^{\frac{5}{2}} + \frac{x ^{3}}{3} + C

\int (x^{2} + x + 1) e^{3 x} d x

\int (2 x + 3) x^{2} + 3 x + 5 d x

\int x^{5} - 3 x + \frac{2}{x} d x

\int \frac{1 + 2 y ^{2}}{y} d y

\int csc (x) \frac{1}{x} d x

What is the integral of (sqrt(x)-x)^2 ?
The integral of (sqrt(x)-x)^2 is (x^2)/2-4/5 x^{5/2}+(x^3)/3+C