DLMF:4.10.E12 (Q1627)

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DLMF:4.10.E12
No description defined

    Statements

    Defining formula
    ∫ 0 ln ⁡ 2 x ⁢ e x e x - 1 ⁢ d x = π 2 12 , superscript subscript 0 2 𝑥 superscript 𝑒 𝑥 superscript 𝑒 𝑥 1 𝑥 superscript 𝜋 2 12 {\displaystyle{\displaystyle\int_{0}^{\ln 2}\frac{xe^{x}}{e^{x}-1}\mathrm{d}x=% \frac{\pi^{2}}{12},}}
    0 references
    DLMF id
    DLMF:4.10.E12
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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.m2acdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aidec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1bdec
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