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