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Topic: Mathematica integration Vs Sympy
Replies: 7   Last Post: Apr 23, 2013 9:38 PM

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Richard Fateman

Posts: 1,539
Registered: 12/7/04
integral of x^n
Posted: Apr 23, 2013 12:02 AM
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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
> 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.


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