rotten news relay - sci.math.symbolic - Re: An interesting rational integral in Mathematica

Subject: Re: An interesting rational integral in Mathematica
From: clicliclic@freenet.d
Newsgroups: sci.math.symbolic
Organization: Killfiles, Unlimited
Date: Sat, 13 Jan 2024 09:29 UTC
References: 1

Path: eternal-september.org!news.eternal-september.org!feeder3.eternal-september.org!nntp-feed.chiark.greenend.org.uk!ewrotcd!news.killfile.org!.POSTED.port-212-4-179-246.dynamic.as20676.net!not-for-mail
From: nobody@nowhere.invalid (clicliclic@freenet.de)
Newsgroups: sci.math.symbolic
Subject: Re: An interesting rational integral in Mathematica
Date: Sat, 13 Jan 2024 10:29:11 +0100
Organization: Killfiles, Unlimited
Message-ID: <65A257E7.E75393D@nowhere.invalid>
References: <b3d304f9-640f-45b2-9cf6-24e7e2853753n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
Injection-Info: flea.killfile.org; posting-host="port-212-4-179-246.dynamic.as20676.net:212.4.179.246";
logging-data="276067"; mail-complaints-to="news@news.killfile.org"
X-Mailer: Mozilla 4.75 [de] (Win98; U)
X-Accept-Language: de

View all headers

Sam Blake schrieb:
>
> Some of you may find this result interesting...
>
> In[1047]:= $Version
>
> Out[1047]= "13.2.0 for Mac OS X x86 (64-bit) (November 18, 2022)"
>
> In[1048]:= Integrate[(2 - Sqrt[7] x^2 + 3 x^4)/(2 + Sqrt[7] x^2 - x^4)^2, x]
>
> Out[1048]= 1/60 (30 x AppellF1[1/2, 2, 2, 3/2, (2 x^2)/(Sqrt[7] + Sqrt[15]), (2 x^2)/(Sqrt[7] - Sqrt[15])] -
> 5 Sqrt[7] x^3 AppellF1[3/2, 2, 2, 5/2, (2 x^2)/(Sqrt[7] + Sqrt[15]), (2 x^2)/(Sqrt[7] - Sqrt[15])] +
> 9 x^5 AppellF1[5/2, 2, 2, 7/2, (2 x^2)/(Sqrt[7] + Sqrt[15]), (2 x^2)/(Sqrt[7] - Sqrt[15])])
>

Acording to Derive 6.10, the antiderivative is simply:

INT((2 - SQRT(7)*x^2 + 3*x^4)/(2 + SQRT(7)*x^2 - x^4)^2, x)

- x/(x^4 - SQRT(7)*x^2 - 2)

Martin.

Subject	Author
Re: An interesting rational integral in Mathematica	clicliclic@freenet.de

You will outgrow your usefulness.

sci / sci.math.symbolic / Re: An interesting rational integral in Mathematica