DLMF:4.10.E9 (Q1624): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1edec

Revision as of 18:15, 1 January 2020

No description defined
Language Label Description Also known as
English
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
    0 references
    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
    0 references
    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
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q1624&oldid=26931"