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Topic: optimal antiderivative for 1/((x^2+x+1)*SQRT(x^2-x+1))
Replies: 13   Last Post: Oct 23, 2011 4:29 PM

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 clicliclic@freenet.de Posts: 1,245 Registered: 4/26/08
optimal antiderivative for 1/((x^2+x+1)*SQRT(x^2-x+1))
Posted: Oct 15, 2011 4:09 AM

Derive 6.10 returns these elementary integrals unevaluated:

INT(1/((x^2 + x + 1)*SQRT(x^2 - x + 1)), x)

INT(x/((x^2 + x + 1)*SQRT(x^2 - x + 1)), x)

The optimal antiderivatives are:

ATANH(SQRT(6)*(x - 1)/(3*SQRT(x^2 - x + 1)))/SQRT(6)
+ ATAN(SQRT(2)*(x + 1)/SQRT(x^2 - x + 1))/SQRT(2)

ATANH(SQRT(6)*(x - 1)/(3*SQRT(x^2 - x + 1)))/SQRT(6)
- ATAN(SQRT(2)*(x + 1)/SQRT(x^2 - x + 1))/SQRT(2)

Is there an integrator clever enough to find them?

Martin.

Date Subject Author
10/15/11 clicliclic@freenet.de
10/15/11 Axel Vogt
10/15/11 G. A. Edgar
10/15/11 clicliclic@freenet.de
10/16/11 Richard Fateman
10/18/11 Waldek Hebisch
10/23/11 clicliclic@freenet.de
10/23/11 Waldek Hebisch
10/18/11 dimmechan@yahoo.com
10/18/11 Richard Fateman
10/21/11 clicliclic@freenet.de
10/21/11 dimmechan@yahoo.com
10/22/11 Albert D. Rich
10/23/11 clicliclic@freenet.de