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I am performing the following integration

Assuming[{r > 0, s > 0, a == 2}, 
 Integrate[s^(2 - a)/Abs[r - s] s^2, s]]

and I get two cases for the output. The first case is:

-r s - s^2/2 - r^2 Log[-r + s], r - s >= 0

The second case is:

r s + s^2/2 + r^2 Log[-r + s], True

I don't know how to interpret the second case. What does Mathematica want to tell me by `True'?

Thanks!

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  • $\begingroup$ see Piecewise >> Details in the docs. $\endgroup$
    – kglr
    Commented Mar 3, 2020 at 11:18
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    $\begingroup$ @kglr Thanks! So if I understand correctly, this is the "else" case? So if the first case does not apply, then the second, `True' case will? $\endgroup$
    – Britzel
    Commented Mar 3, 2020 at 11:55
  • $\begingroup$ From the Details section of the doc page: "The cond_i are evaluated in turn, until one of them is found to yield True." So yes, it is the "else" case. $\endgroup$
    – Szabolcs
    Commented Mar 3, 2020 at 12:07
  • $\begingroup$ @Szabolcs Thanks! $\endgroup$
    – Britzel
    Commented Mar 3, 2020 at 12:11

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