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DLMF:4.40.E15 - MaRDI portal

DLMF:4.40.E15 (Q2455)

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DLMF:4.40.E15
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    Statements

    DLMF defining formula
    ∫ arcsech ⁡ x ⁢ d x = x ⁢ arcsech ⁡ x + arcsin ⁡ x , hyperbolic-inverse-secant 𝑥 𝑥 𝑥 hyperbolic-inverse-secant 𝑥 𝑥 {\displaystyle{\displaystyle\int\operatorname{arcsech}x\mathrm{d}x=x% \operatorname{arcsech}x+\operatorname{arcsin}x,}}
    0 references
    constraint
    0 < x < 1 0 𝑥 1 {\displaystyle{\displaystyle 0<x<1}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
    0 references
    inverse hyperbolic secant function
    DLMF defining formula
    arcsech ⁡ z hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}
    xml-id
    C4.S37.E8.m2adec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3andec
    0 references
    Q11213
    DLMF defining formula
    arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m5adec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1ndec
    0 references

    Identifiers

     
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