# Integral cos 3x

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

Series expansion of the integral at x=0 |

x – (3 x^3)/2 + (27 x^5)/40 + O(x^6) (Taylor series) |

Definite integral |

integral_0^(pi/6) cos(3 x) dx = 1/3~~0.333333 |

Definite integral mean square |

integral_0^((2 pi)/3) (3 cos^2(3 x))/(2 pi) dx = 1/2 = 0.5 |