Re: Integration Constants 2

*To*: mathgroup at smc.vnet.net*Subject*: [mg5187] Re: Integration Constants 2*From*: Daniel Lichtblau <danl>*Date*: Sat, 9 Nov 1996 02:24:00 -0500*Organization*: wolfram.com*Sender*: owner-wri-mathgroup at wolfram.com

Dennis Michael Winters wrote: > > I posted a message recently (Integration...Constants) that received > several valuable responses requesting more information. Well, here is > the actual problem: > > In[1]:=Integrate[(-2 x+ao)^-2 (-x+bo)^-1, x] > > Mathematica gives the following output: > > Out[1]=-(1/((ao-2 bo)(ao- 2 x))) - (Log(-bo+x)/(ao^2 - 4 ao bo + 4 bo^2)) + > > Log(-ao + 2 x)/(ao^2 - 4 ao bo + 4 bo^2) > > This answer is incorrect. If performed by hand, the answer is shown to > have positive values for ao and bo. This is confirmed by the fact that > this integration is a classical result of chemistry. Years of chemical > reaction rate analysis show the values to be positive. Again, this > calculation was performed using the unix version of 2.2.3. Any help from > those who have already responded would be most appreciated. > > -- > ---------------------------------- > -Dennis M. Winters - > -P.O. BOX 21215 - > -EMORY UNIVERSITY - > -ATLANTA, GA 30322 - > -dwint01 at emory.edu - > -or winters at euch6h.chem.emory.edu- > ---------------------------------- Below I show the result from version 3.0, which is mathematically equivalent to your result. I then show that the integrand and the differentiated result differ by a constant (which is in fact zero). Out[4]//InputForm= 1/((ao - 2*bo)*(-ao + 2*x)) - Log[-bo + x]/(ao - 2*bo)^2 + Log[-ao + 2*x]/(ao - 2*bo)^2 In[5]:= ee = (-2 x+ao)^-2 (-x+bo)^-1; In[6]:= Integrate[ee, x] // InputForm Out[6]//InputForm= 1/((ao - 2*bo)*(-ao + 2*x)) - Log[-bo + x]/(ao - 2*bo)^2 + Log[-ao + 2*x]/(ao - 2*bo)^2 In[7]:= D[%, x] - ee // Together Out[7]= 0 I do not understand what you mean by the phrase, "answer ... ha[s] positive values for ao and bo". The variables ao and bo are parameters. Daniel Lichtblau Wolfram Research danl at wolfram.com