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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
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