# 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) |