# Integral sin^3

Indefinite integral |
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integral sin^3(x) dx = 1/12 (cos(3 x) – 9 cos(x)) + constant |

Expanded form of the integral |

1/12 cos(3 x) – (3 cos(x))/4 + constant |

Series expansion of the integral at x=0 |

-2/3 + x^4/4 + O(x^6) (Taylor series) |

Definite integral over a half-period |

integral_0^pi sin^3(x) dx = 4/3~~1.33333 |

Definite integral mean square |

integral_0^(2 pi) (sin^6(x))/(2 pi) dx = 5/16 = 0.3125 |