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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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01ln?(ln?x)dx(1+x2)ln?x=1ln?ln?xdx(1+x2)ln?x=πk=0(1)k+12k+1[ln?(2k+1)+2ln?2+C]

si906_e  BI (147)(4)

11. 

01ln?(ln?x)xμ1dxln?x=(C+ln?4μ)πμ[Re?μ>0]

si907_e  BI (147)(3)

12. 

01ln?(ln?x)(ln?x)u1xv1dx=1vμΓ(μ)[ψ(μ)ln?(v)]

si908_e  BI (147)(2)

[Re?μ>0,?Re?v>0]si909_e

4.326

1. 

01ln?(aln?x)xμ1dx=1μ[ln?aeaμEi?(aμ)][Re?μ>0,a>0]

  BI (107)(23)

2. 

01/eln

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