Integral with complications

  • Thread starter rman144
  • Start date
  • #1
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I've looked everywhere for a method or approach to break down this integral, but so far, nothing. If anyone has any ideas or answers, I would be incredibly thankful:


∫ {[ln(v)]^(s-1) - [ln(v)]^(-s)}/(v-1) dv, with limits from v=1 to v=e, and 0<Re(s)<1

I've tried breaking it down to the real and imaginary parts, but even then I was back to the problem of trying to integrate with cos(u)+isin(u) issues.
 

Answers and Replies

  • #2
534
1
[tex]\int_1^e \frac{(\ln v)^{s - 1} - (\ln v)^{-s}}{v - 1} \,dv

According to Mathematica, the integral doesn't converge. It doesn't seem to be able to find an indefinite integral either.
 

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