x^(1/3)-x
Assuming the principal root | Use instead

Input

x^(1/3) - x

Alternate form

(1 - x^(2/3)) x^(1/3)
-((x^(1/3) - 1) (x^(1/3) + 1) x^(1/3))

Roots

x = 0
x = 1

Properties as a real function

Domain

{x element R : x>=0} (all non-negative real numbers)

Range

{y element R : y<=2/(3 sqrt(3))}

Derivative

d/dx(x^(1/3) - x) = 1/(3 x^(2/3)) - 1

Indefinite integral

integral(x^(1/3) - x) dx = (3 x^(4/3))/4 - x^2/2 + constant
POWERED BY THE WOLFRAM LANGUAGE