# Cosx^2 integral

Indefinite integral |
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integral cos^2(x) dx = 1/2 (x + sin(x) cos(x)) + constant |

Expanded form of the integral |

x/2 + 1/2 sin(x) cos(x) + constant |

Series expansion of the integral at x=0 |

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

Series expansion of the integral at x=∞ |

1/4 ((2 x + O((1/x)^13)) + sin(2 x)) |

Definite integral over a half-period |

integral_0^(pi/2) cos^2(x) dx = pi/4~~0.785398 |

Definite integral over a period |

integral_0^pi cos^2(x) dx = pi/2~~1.5708 |

Definite integral mean square |

integral_0^pi (cos^4(x))/pi dx = 3/8 = 0.375 |