DLMF:4.10.E3 (Q1618)

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DLMF:4.10.E3
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    Statements

    Defining formula
    ∫ z n ⁢ ln ⁡ z ⁢ d z = z n + 1 n + 1 ⁢ ln ⁡ z - z n + 1 ( n + 1 ) 2 , superscript 𝑧 𝑛 𝑧 𝑧 superscript 𝑧 𝑛 1 𝑛 1 𝑧 superscript 𝑧 𝑛 1 superscript 𝑛 1 2 {\displaystyle{\displaystyle\int z^{n}\ln z\mathrm{d}z=\frac{z^{n+1}}{n+1}\ln z% -\frac{z^{n+1}}{(n+1)^{2}},}}
    0 references
    DLMF id
    DLMF:4.10.E3
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    constraint
    n ≠ - 1 𝑛 1 {\displaystyle{\displaystyle n\neq-1}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
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    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1dec
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    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1bdec
    0 references
     
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