# Integrate cos4x

Indefinite integral |
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integral cos(4 x) dx = 1/4 sin(4 x) + constant |

Series expansion of the integral at x=0 |

x – (8 x^3)/3 + (32 x^5)/15 + O(x^6) (Taylor series) |

Definite integral |

integral_0^(pi/8) cos(4 x) dx = 1/4 = 0.25 |

Definite integral mean square |

integral_0^(pi/2) (2 cos^2(4 x))/pi dx = 1/2 = 0.5 |