Get the result of an integral as it appears in a paper?

Questions
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1

Hi guys:

I am reading a paper these days, as in the attachment. The author of paper use Maple for calculation, however, when I tried on Mathematica. Quite often I failed to get a result and in most cases, maple offer a better solution. Following is one case:

Case1.png
Case1.png1031×309 3.62 KB

I tied in the Mathematica, but the result is a bit disappointing:

MathematicaResult.png
MathematicaResult.png706×298 5.61 KB

I guess most of us would prefer the result in the paper, which is done by maple rather than Mathematica. So I am wondering how to get the result exactly like that by Mathematica?

2

you have typo inside of integral.. see attachment

3

Thanks for pointing this out. I corrected it now. Although the result is still not the same, (only difference is with the sign), I would prefer the result is wrong.

4

You can get Mathematica to combine the two logs using assumptions in FullSimplify:

With[{c = 1/100},
 result1 = (1 + c*t) Exp[-c*t] + 
   c^2 (1 - s*Exp[-c*t]) Integrate[(1 - s*Exp[-c*v])^-2 v*
      Exp[-c*v], {v, 0, t}];
 result2 = FullSimplify[result1, 1 - s > 0 && E^(t/100) - s > 0];
 Collect[result2, _Log, Simplify]]
5

Dear Professor?

I followed your way to calculate the following integral, however, the result does not combine this time. May I ask why is that and how can I improve that? Quite obviously that Ln part could be collected:

3078MathematicaResult.png
3078MathematicaResult.png976×262 8.89 KB

I upload the nb file in the attachment. Really need your help.