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DLMF:4.10.E9 - MaRDI portal

DLMF:4.10.E9 (Q1729)

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DLMF:4.10.E9
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    Statements

    DLMF 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
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2agdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1edec
    0 references
    complex
    DLMF defining formula
    a ≠ 0 𝑎 0 {\displaystyle{\displaystyle a\neq 0}}
    xml-id
    C4.S10.XMD1.m1adec
    0 references
    complex
    DLMF defining formula
    b ≠ 0 𝑏 0 {\displaystyle{\displaystyle b\neq 0}}
    xml-id
    C4.S10.XMD2.m1dec
    0 references

    Identifiers

     
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