Trouble with Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg39264] Trouble with Integrate*From*: "Marko Vojinovic" <vojinovi at panet.co.yu>*Date*: Thu, 6 Feb 2003 03:08:30 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: Trouble with Integrate***From:*Dr Bob <drbob@bigfoot.com>