Can anyone solve this complicated integral with limited conditions?

[rman144]

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.

 

[adriank]

\int_1^e \frac{(\ln v)^{s - 1} - (\ln v)^{-s}}{v - 1} \,dv<br /> <br /> According to Mathematica, the integral doesn&#039;t converge. It doesn&#039;t seem to be able to find an indefinite integral either.