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 » Software » comp.soft-sys.math.mathematica

Topic: Difficult antiderivative
Replies: 4   Last Post: Dec 3, 2012 3:38 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Alexei Boulbitch

Posts: 483
Registered: 2/28/08
Re: Difficult antiderivative
Posted: Dec 3, 2012 3:18 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


Q.: may be that the antiderivative does not exist?

The numerical integral (b<r<a)

NIntegrate[ ArcCosh[a/x]/Sqrt[r^2-x^2],{x,b,r}]

Don't give any problem.

Any help very appreciated (and considered).

Cheers, Rob

Hi, Rob,

Yes, it is a general case that indefinite integrals cannot be expressed in
terms of some finite combination of analytical and special functions. That
is a more mathematically correct expression of the thing you obviously have
in mind when writing "does not exist".

Even more, most of indefinite integrals have this property, and only smaller part of them can be expressed in terms of analytical and special functions. It is also common that the indefinite integral "does not exist" (using your expression), while the definite one does.

Have fun, Alexei


Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG

Office phone : +352-2454-2566
Office fax: +352-2454-3566
mobile phone: +49 151 52 40 66 44

e-mail: alexei.boulbitch@iee.lu<mailto:alexei.boulbitch@iee.lu>




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.