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Re: Difficult antiderivative

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  • Subject: [mg128833] Re: Difficult antiderivative
  • From: Alexei Boulbitch <Alexei.Boulbitch at>
  • Date: Thu, 29 Nov 2012 06:06:06 -0500 (EST)
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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.
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