DLMF:4.26.E3 (Q1819)

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DLMF:4.26.E3
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    Statements

    Defining formula
    ∫ tan ⁡ x ⁢ d x = - ln ⁡ ( cos ⁡ x ) , 𝑥 𝑥 𝑥 {\displaystyle{\displaystyle\int\tan x\mathrm{d}x=-\ln\left(\cos x\right),}}
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    DLMF id
    DLMF:4.26.E3
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    constraint
    - 1 2 ⁢ π < x < 1 2 ⁢ π 1 2 𝜋 𝑥 1 2 𝜋 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi<x<\tfrac{1}{2}\pi}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
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