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) |