Re: [Q] Why Integrate[1/x,x] <> Log[Abs[x]] with Mma 2.2 ?

• To: mathgroup at smc.vnet.net
• Subject: [mg8788] Re: [Q] Why Integrate[1/x,x] <> Log[Abs[x]] with Mma 2.2 ?
• From: "Stephen P Luttrell" <luttrell at signal.dra.hmg.gb>
• Date: Thu, 25 Sep 1997 12:26:22 -0400
• Organization: Defence Evaluation and Research Agency
• Sender: owner-wri-mathgroup at wolfram.com

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Denis Barbier <barbier at cmapx.polytechnique.fr> wrote in article
<5vt7q9\$ghc at smc.vnet.net>...
> it is well known that Integrate[1/x,x] = Log[Abs[x]], but Mma 2.2 returns
> Log[x].
>
> How can i correct this ?

I have checked that the following works correctly in Mathematica 3.0. I
don't know whether version 2.2 will behave in the same way.

Log[x] is the correct result, where x is a complex number.

If you want to evaluate the definite integral between two points on the
positive real line (which is what I suspect you want to do - correct me if
I'm wrong), then Log[x2]-Log[x1] will give the same result as
Log[Abs[x2]]-Log[Abs[x1]].

If you want to evaluate the integral along a piecewise linear contour whose
corners are specified by the list {x1,x2,...,xn}, where the xi are complex
numbers, then evaluate Integrate[1/x,{x,x1,x2,...,xn}]. For instance,
Integrate[1/x,{x,1,I,-1,-I,1}] will yield the result 2 I \[Pi], as
expected.

--
Stephen P Luttrell
luttrell at signal.dra.hmg.gb