# Integral of 1/cosx

Indefinite integral |
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integral 1/(cos(x)) dx = log(tan(x) + sec(x)) + constant |

Series expansion of the integral at x=0 |

x + x^3/6 + x^5/24 + O(x^6) (Taylor series) |

Series expansion of the integral at x=-(3 π)/2 |

(-log(x + (3 pi)/2) + i pi + log(2)) – 1/12 (x + (3 pi)/2)^2 – (7 (x + (3 pi)/2)^4)/1440 + O((x + (3 pi)/2)^6) (generalized Puiseux series) |

Series expansion of the integral at x=-π/2 |

log(1/4 (2 x + pi)) + 1/12 (x + pi/2)^2 + (7 (x + pi/2)^4)/1440 + O((x + pi/2)^6) (generalized Puiseux series) |

Series expansion of the integral at x=π/2 |

(-log(x – pi/2) – i pi + log(2)) – 1/12 (x – pi/2)^2 – (7 (x – pi/2)^4)/1440 + O((x – pi/2)^6) (generalized Puiseux series) |

Series expansion of the integral at x=(3 π)/2 |

log(1/4 (2 x – 3 pi)) + 1/12 (x – (3 pi)/2)^2 + (7 (x – (3 pi)/2)^4)/1440 + O((x – (3 pi)/2)^6) (generalized Puiseux series) |