       Re: Re: Integrate Bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg13248] Re: [mg13218] Re: Integrate Bug?
• From: David Withoff <withoff>
• Date: Fri, 17 Jul 1998 03:17:44 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```> Examining the difference in the terms produced, the "bug" is much easier
> to reproduce
>
> In:= awm = Log[1-W]
>
> Out= Log[1 - W]
>
> In:= Integrate[D[awm,W],W]
>
> Out= Log[-1 + W]
>
> But if you do the integration normally, the answer is "Log[Abs[-1 +
> W]]." Since Mathematica
> can't know what the value of W (or b Nt W in your case) is, it seems to
> assume > 1.  I would
> just use /. Log[a_] :> Log[Abs[a_]] before making your numerical
> substitutions.
>
> Alan

The assumption made by Mathematica is that Log refers to the general
complex logarithm function.  With that, an assumption about the value
of W isn't needed.  The result is correct for all values of W except
when W is 1, where it is undefined.

For general complex functions, Log[Abs[-1 + W]] is an incorrect result.
Abs is not a differentiable as a function of a complex argument, and so
couldn't be part of an indefinite integral (antiderivative).

Presumably "do the integration normally" means doing the calculation
with the assumption that everything is real, that differentiation
refers to directional differentiation along the real axis, and so
forth.

Dave Withoff
Wolfram Research

```

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