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Re: Difficult antiderivative
*To*: mathgroup at smc.vnet.net
*Subject*: [mg128833] Re: Difficult antiderivative
*From*: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
*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.
IEE S.A.
ZAE Weiergewan,
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L-5326 Contern, LUXEMBOURG
Office phone : +352-2454-2566
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e-mail: alexei.boulbitch at iee.lu<mailto:alexei.boulbitch at iee.lu>
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