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I calculate such limit with *Mathematica*:

```
Limit[(Log[u] (Log[1 + (2 u)/(I - 2 t)] - Log[1 - (2 u)/(I + 2 t)]) +
PolyLog[2, (2 u)/(-I + 2 t)] - PolyLog[2, (2 u)/(I + 2 t)]),
u -> ∞]
```

`1/2 (-Log[2/(I - 2 t)]^2 + Log[-(2/(I + 2 t))]^2).`

I would like to know the calculation steps. *Wolfram Alpha* gives no answer.

Have you tried

`Trace`

? – Mike Honeychurch – 2013-11-20T07:50:11.597Yes. It wasn't helpful. – Fancier of Mathematica – 2013-11-20T08:34:22.883

Generally Mathematica doesn't provide intermediate steps. You're probably out of luck here. – Sjoerd C. de Vries – 2013-11-20T09:37:33.833

2Limit will attempt to form a series at infinity. In some cases it can then deduce limiting behavior. In more extreme cases it may need to resort to an exp-log (hierarchical) series. – Daniel Lichtblau – 2013-11-20T16:17:43.947