DLMF:4.40.E11 (Q1983): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1ajdec
Property / Symbols used
 
Property / Symbols used: Q11247 / rank
 
Normal rank
Property / Symbols used: Q11247 / qualifier
 
test:

arcsinh z hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}

\asinh@@{\NVar{z}}
Property / Symbols used: Q11247 / qualifier
 
xml-id: C4.S37.SS2.p1.m8adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3ajdec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1jdec

Latest revision as of 18:23, 1 January 2020

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DLMF:4.40.E11
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    Statements

    arcsinh x d x = x arcsinh x - ( 1 + x 2 ) 1 / 2 . hyperbolic-inverse-sine 𝑥 𝑥 𝑥 hyperbolic-inverse-sine 𝑥 superscript 1 superscript 𝑥 2 1 2 {\displaystyle{\displaystyle\int\operatorname{arcsinh}x\mathrm{d}x=x% \operatorname{arcsinh}x-(1+x^{2})^{1/2}.}}
    0 references
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1ajdec
    0 references
    arcsinh z hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}
    C4.S37.SS2.p1.m8adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3ajdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1jdec
    0 references