Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.symbolic.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
clicliclic@freenet.de

Posts: 959
Registered: 4/26/08
optimal antiderivative for 1/((x^2+x+1)*SQRT(x^2-x+1))
Posted: Oct 15, 2011 4:09 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


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.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.