On 4/22/2013 12:13 AM, Alex Krasnov wrote: > In this case, the results are valid for a=1 in the sense of a limit, as > Limit[u, a -> 1] and limit(u, a, 1) demonstrate. This is not always the > case. Example: > > In: f = Integrate[x^n, x] > Out: x^(1 + n)/(1 + n) > > In: Limit[f, n -> -1, Direction -> 1] > Out: -Infinity > > In: Limit[f, n -> -1, Direction -> -1] > Out: Infinity > > Alex > >
Yes, but an equally valid antiderivative for x^n is
s = (x^(n+1)-1)/(n+1).
Limit[s,n->-1] is Log[x].
This alternative formula was, I think, pointed out more than once to Wolfram Inc. probably circa version 2.
There are other issues that come up when using antiderivatives + the fundamental theorem of integral calculus. Some of these become apparent by reading FTIC carefully.