Re: Integrate[1/x, x] ??

• To: mathgroup at smc.vnet.net
• Subject: [mg29923] Re: [mg29919] Integrate[1/x, x] ??
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Thu, 19 Jul 2001 03:56:51 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

As for the constant: yes, but Mathematica's Integrate leaves it out as you
can find in the documention. On the other hand:

In[8]:=
DSolve[Derivative[1][y][x] == 1/x, y, x]

Out[8]=
{{y -> Function[{x}, C[1] + Log[x]]}}

gives you the constant if you desperately need it.

As for the rest of your question, the answer depends on how much mathematics
you know. If you only know about real numbers and believe that, say, Log[-5]
does not exist than yes. But Mathematica knows about complex numbers so it
gives:

In[13]:=
Log[-5]

Out[13]=
I Pi + Log[5]

In short, Mathematica's answer is more general than yours, but to explain it
fully would take several lectures on complex functions.

--
Andrzej Kozlowski
Toyama International University
JAPAN

http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/~andrzej/

on 01.7.18 3:08 PM, Tim 9-23 at bendoftimeb at stny.rr.com wrote:

>
> ln(abs(x))+C
>
> and not log(x).
>
> My email address is anti-spammed.  Remove the 2 B's after hitting email reply
> if you want to email me.
>
> Tim 9-23
>
>

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