Cubed root of x^9

Cubed root of x^9

Input
cuberoot(x^9)
Result
(x^9)^(1/3)
Alternate form
x^3
Root
x = 0
Series expansion at x=0
piecewise | piecewise | -(-x^9)^(1/3) + O(x^17) | Im(x^9)<=0 -(-x^9)^(1/3)^* + O(x^17) | (otherwise) | x<=0 (x^9)^(1/3) + O(x^10) | (otherwise)
Series expansion at x=∞
piecewise | x^3 + O((1/x)^13) | 1/x>0
-(-x^9)^(1/3) + O((1/x)^10) | (otherwise)
Derivative
d/dx(cuberoot(x^9)) = (3 x^8)/(x^9)^(1/3)^2
Indefinite integral
integral cuberoot(x^9) dx = 1/4 x (x^9)^(1/3) + constant
Series representation
(x^9)^(1/3) = sum_(n=0)^infinity (script c)_n (-1 + x)^n for ((script c)_0 = 1 and (-3 + n) (script c)_n + (1 + n) (script c)_(1 + n) = 0)

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