Re: Mathematica gives bad integral ??

*To*: mathgroup at smc.vnet.net*Subject*: [mg24324] Re: Mathematica gives bad integral ??*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sun, 9 Jul 2000 04:52:34 -0400 (EDT)*Organization*: Universitaet Leipzig*References*: <8k3n38$3pk@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I don't know an explanation because ires = FullSimplify[Integrate[1/Sqrt[1 - Sin[2x]], x]]; (ArcTanh[(1 + Tan[x/2])/Sqrt[2]]*(Cos[x] - Sin[x]))/ Sqrt[1/2 - Cos[x]*Sin[x]] and D[ires, x] // FullSimplify gives 1/Sqrt[1 - Sin[2*x]] Since you don't supply any Input I can only tell you that Mathematica has no error. Regards Jens "J.R. Chaffer" wrote: > > Hi, this newbie gets erroneous results with Mathematica > 4.0 (for students), with the following integral. Hopefully > someone can tell me why, and what I may be doing > wrong. I have tried "Assumptions -> x e Reals", or > x > 0, with same results. Integral in question is, > > Integrate[1/Sqrt[1-Sin[2x]]] > > The result is somewhat involved, instead of the expected > result (Schaum, "Calculus" 4E, p. 297), > > integral = - (1/Sqrt[2])Log[Abs[Csc[Pi/4-x]-Cot[Pi/4-x]]] > > One expects to get differing forms with any computer > algebra system, since there are so many equivalent forms > of algebraic expressions. However, Mathematica's form > and the Schaum (correct) form differ by significant > numerical values, as plotting shows (i.e., not some E-16 > or some such). > > Further, and what really seems wrong, is that when one > differentiates Mathematica's result for the integral, one > does NOT get the original integrand, or anything even > close, numerically. > > So, I am confused. Anyone who knows the explanation > would be welcome to share it. > > Thank you. > > John Chaffer