Re: Trouble with Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg39275] Re: [mg39264] Trouble with Integrate*From*: Dr Bob <drbob at bigfoot.com>*Date*: Fri, 7 Feb 2003 03:08:02 -0500 (EST)*References*: <200302060808.DAA09215@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

With version 4.2 I get the same answers as you for Integrate[f, {x, 0, Infinity}] and NIntegrate[f, {x, 0, Infinity}], but Integrate[1/(Sqrt[1 + x^4] + x^2), {x, 0, Infinity}] is not evaluated. Bobby On Thu, 6 Feb 2003 03:08:30 -0500 (EST), Marko Vojinovic <vojinovi at panet.co.yu> wrote: > Consider the function: > > f = Sqrt[1+x^4] -x^2 > > Upon asking to > > Integrate[f,{x,0,Infinity}] > > Mathematica 4.0 answers: > > -Infinity > > which is not correct. However, > > NIntegrate[f,{x,0,Infinity}] > > gives the correct (numerical) answer: > 1.23605 > > The correct (analytical, i.e.. exact) answer to the integral is: > > Gamma[1/4] Gamma[1/4] / 6 Sqrt[Pi] > > which can be obtained after some paperwork. However, if I ask > > Integrate[1/(Sqrt[1+x^4] + x^2),{x,0,Infinity}] > > (this integrand is equivalent to f) one gets a complicated answer in > terms > of EllipticF. Meanwhile, when I ask Mathematica 3.0 the same set of > questions, I get correct answers, and analytical integration gives answer > in > terms of Gamma. Two questions: > > 1) Why does version 4.0 give so fairly incorrect result "-Infinity" for > the > first integral? > 2) How can I 'switch off' the use of elliptic functions and/or 'force' > Mathematica to use Gamma? > > Thanks, > Marko > > > > > > > > > -- majort at cox-internet.com Bobby R. Treat

**References**:**Trouble with Integrate***From:*"Marko Vojinovic" <vojinovi@panet.co.yu>