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DLMF:4.10.E13 - MaRDI portal

DLMF:4.10.E13 (Q1737)

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DLMF:4.10.E13
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    Statements

    DLMF defining formula
    ∫ 0 ∞ d x e x + 1 = ln ⁡ 2 . superscript subscript 0 𝑥 superscript 𝑒 𝑥 1 2 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\mathrm{d}x}{e^{x}+1}=\ln 2% .}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2ajdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1cdec
    0 references

    Identifiers

     
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