# Cos^3x integral

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

Expanded form of the integral |

(3 sin(x))/4 + 1/12 sin(3 x) + constant |

Series expansion of the integral at x=0 |

x – x^3/2 + (7 x^5)/40 + O(x^6) (Taylor series) |

Definite integral |

integral_0^(pi/2) cos^3(x) dx = 2/3~~0.666667 |

Definite integral mean square |

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