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Re: Integration..Constants

• To: mathgroup at smc.vnet.net
• Subject: [mg5190] Re: [mg5119] Integration..Constants
• From: "C. Woll" <carlw at u.washington.edu>
• Date: Thu, 14 Nov 1996 02:02:01 -0500
• Sender: owner-wri-mathgroup at wolfram.com

On Wed, 30 Oct 1996, Dennis Michael Winters wrote:

> I have tried several times to perform an integration(math..2.2.3)B 
> similar to the following.
> 
> In[1]:=Integrate[(ao+x)^-1 (bo^-2), x]
> 
> The results, however, are always incorrect:
> 
> Out[1]=-ln(-ao+x)  <---where the constant "ao" should be positive.
> 
> ... more stuff

Dennis,

It seems to me that you made a typo in your question. Specifically, if you
give Mma the integral

In[1]:=Integrate[(ao-x)^-1, x]

then you probably get (I haven't checked this on Mma myself)

Out[1]:=-ln[-ao+x]

But, try taking a derivative of this, you get the expected answer. You
might have expected to get

Out[1]:= -ln[ao-x]

and, naturally enough, if you take a derivative of this, you get the
expected answer. So, what's going on? Well, these two answers differ by a
constant:

-ln[-ao+x] = -ln[ (-1) (ao-x) ] = -ln[-1] - ln[ao-x]

and

-ln[-1] = -ln[ Exp[I Pi] ] = - I Pi

Thus, Mma is not doing anything wrong here.

Carl
Physics Dept
U of Washington

carlw at u.washington.edu