DLMF:4.26.E16 (Q1832): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10816 / rank
 
Normal rank
Property / Symbols used: Q10816 / qualifier
 
Defining formula:

arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

\atan@@{\NVar{z}}
Property / Symbols used: Q10816 / qualifier
 
xml-id: C4.S23.SS2.p1.m7adec
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.m2acdec
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.m1jdec

Latest revision as of 18:42, 1 January 2020

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DLMF:4.26.E16
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    Statements

    arctan x d x = x arctan x - 1 2 ln ( 1 + x 2 ) , 𝑥 𝑥 𝑥 𝑥 1 2 1 superscript 𝑥 2 {\displaystyle{\displaystyle\int\operatorname{arctan}x\mathrm{d}x=x% \operatorname{arctan}x-\tfrac{1}{2}\ln\left(1+x^{2}\right),}}
    0 references
    DLMF:4.26.E16
    0 references
    - < x < 𝑥 {\displaystyle{\displaystyle-\infty<x<\infty}}
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aodec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aodec
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    arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    C4.S23.SS2.p1.m7adec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2acdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1jdec
    0 references