RE: Please help overcome problems with integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg72254] RE: [mg72229] Please help overcome problems with integration*From*: "David Park" <djmp at earthlink.net>*Date*: Sat, 16 Dec 2006 05:18:24 -0500 (EST)

Aaron, I'm not certain why you insist on working with the general indefinite integral. The indefinite integral always has a possible implied constant that must be added. Furthermore the result contains an ArcTan function which is a multifunction. The general result for ArcTan[x] should be ArcTan[x] + n Pi where n is an integer. If you look at your specific case you will see that you have the term -0.463512 ArcTan[0.0224733 (102 - 96 x)] If you use Chop to get rid of the imaginary part of the first answer then you can compare the two answers with the n Pi term, and calculate the value of n by... 1.6552 == -1.25713 + n*Pi*-0.46351240544347894; Solve[%] {{n -> -2.}} And you see the two answers are the same if you take the proper multivalue for ArcTan. Either go with integrating specific cases, or try to find some method of picking the correct multivalue for ArcTan, which may be extremely difficult. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: aaronfude at gmail.com [mailto:aaronfude at gmail.com] Hi, This is similar to my previous posts, but I have worked hard to come up with the simplest possible example which highlights what ought to be considered in bug in Mathematica. Please comment and suggest a work around. F = Log[(-1 + d x + e Sqrt[f + 2g x + h x^2])]; st = Integrate[F, x]; specific = st /. { d -> -2, e -> 10, f -> 1.3, g -> -1, h -> 1 }; (specific /. x -> 1 ) - (specific /. x -> 0) NIntegrate[F /. { d -> -2, e -> 10, f -> 1.3, g -> -1, h -> 1 }, {x, 0, 1}] The results are: -1.25713 - 4.44^-16*I and 1.6552 Thank you very much in advance! Aaron Fude