DLMF:4.10.E9 (Q1624)

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DLMF:4.10.E9
No description defined

    Statements

    Defining formula
    ∫ d z e a ⁢ z + b = 1 a ⁢ b ⁢ ( a ⁢ z - ln ⁡ ( e a ⁢ z + b ) ) , 𝑧 superscript 𝑒 𝑎 𝑧 𝑏 1 𝑎 𝑏 𝑎 𝑧 superscript 𝑒 𝑎 𝑧 𝑏 {\displaystyle{\displaystyle\int\frac{\mathrm{d}z}{e^{az}+b}=\frac{1}{ab}(az-% \ln\left(e^{az}+b\right)),}}
    0 references
    DLMF id
    DLMF:4.10.E9
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2agdec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1edec
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    Q11228
    Defining formula
    a ≠ 0 𝑎 0 {\displaystyle{\displaystyle a\neq 0}}
    xml-id
    C4.S10.XMD1.m1adec
    0 references
    Q11229
    Defining formula
    b ≠ 0 𝑏 0 {\displaystyle{\displaystyle b\neq 0}}
    xml-id
    C4.S10.XMD2.m1dec
    0 references
     
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