integral of x^n
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- Subject: [mg130575] integral of x^n
- From: Richard Fateman <fateman at cs.berkeley.edu>
- Date: Tue, 23 Apr 2013 00:03:24 -0400 (EDT)
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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
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.
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