DLMF:4.10.E10 (Q1625)

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DLMF:4.10.E10
No description defined

    Statements

    Defining formula
    ∫ e a ⁢ z - 1 e a ⁢ z + 1 ⁢ d z = 2 a ⁢ ln ⁡ ( e a ⁢ z / 2 + e - a ⁢ z / 2 ) , superscript 𝑒 𝑎 𝑧 1 superscript 𝑒 𝑎 𝑧 1 𝑧 2 𝑎 superscript 𝑒 𝑎 𝑧 2 superscript 𝑒 𝑎 𝑧 2 {\displaystyle{\displaystyle\int\frac{e^{az}-1}{e^{az}+1}\mathrm{d}z=\frac{2}{% a}\ln\left(e^{az/2}+e^{-az/2}\right),}}
    0 references
    DLMF id
    DLMF:4.10.E10
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2ahdec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1fdec
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    Q11228
    Defining formula
    a ≠ 0 𝑎 0 {\displaystyle{\displaystyle a\neq 0}}
    xml-id
    C4.S10.XMD1.m1bdec
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