DLMF:4.26.E3 (Q1819): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: tangent function / rank
 
Normal rank
Property / Symbols used: tangent function / qualifier
 
Defining formula:

tan z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}

\tan@@{\NVar{z}}
Property / Symbols used: tangent function / qualifier
 
xml-id: C4.S14.E4.m2adec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1bdec

Latest revision as of 18:40, 1 January 2020

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DLMF:4.26.E3
No description defined

    Statements

    tan x d x = - ln ( cos x ) , 𝑥 𝑥 𝑥 {\displaystyle{\displaystyle\int\tan x\mathrm{d}x=-\ln\left(\cos x\right),}}
    0 references
    DLMF:4.26.E3
    0 references
    - 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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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2abdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1abdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3abdec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2adec
    0 references
    tan z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    C4.S14.E4.m2adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1bdec
    0 references