DLMF:1.4.E17 (Q96)

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DLMF:1.4.E17
No description defined

    Statements

    Defining formula
    ∫ x n ⁢ d x = { x n + 1 n + 1 + C , n ≠ - 1 , ln ⁡ | x | + C , n = - 1 . superscript 𝑥 𝑛 𝑥 cases superscript 𝑥 𝑛 1 𝑛 1 𝐶 𝑛 1 𝑥 𝐶 𝑛 1 {\displaystyle{\displaystyle\int x^{n}\mathrm{d}x=\begin{cases}\dfrac{x^{n+1}}% {n+1}+C,&\quad n\not=-1,\\ \ln\left|x\right|+C,&\quad n=-1.\end{cases}}}
    0 references
    DLMF id
    DLMF:1.4.E17
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
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    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1cdec
    0 references
    Q10772
    Defining formula
    C 𝐶 {\displaystyle{\displaystyle C}}
    xml-id
    C1.S4.XMD3.m1dec
    0 references
     
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