4.25 Combinations of logarithms and powers

4.251

1 

0xμ1ln?xβ+x?dx=πβμ1sin?μπ(ln?βπcot?μπ)[|arg?β|?<π,?0<Re?μ<1]

si370_e  BI (135)(1)

2. 

0xμ1ln?xaxdx=πaμ1?(cot?μπ?ln?aπsin2μπ)[a>?0,?0<Re?μ<1]

si371_e  ET I 314(5)

3.10 

01xμ1ln?xx+1dx=β'(μ)[Re?μ>0]

si372_e  GW (324)(6), ET I 314(3)

4. 

01xμ1ln?xx1dx=ψ'(μ)=ζ(2,μ)[Re?μ>0]

si373_e  BI (108)(8)

5.11 

01ln

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