Difficult antiderivative
- To: mathgroup at smc.vnet.net
- Subject: [mg128811] Difficult antiderivative
- From: "Brambilla Roberto Luigi (RSE)" <Roberto.Brambilla at rse-web.it>
- Date: Wed, 28 Nov 2012 03:15:14 -0500 (EST)
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Using Mathematica (v5.1 to v.8) it is possible to obtain (in few
seconds) the following antiderivative
(1) Integrate[ x ArcCosh[a/x]/Sqrt[r^2-x^2],x]
(a rather lengthy expression).
It happens that I need
(2) Integrate[ ArcCosh[a/x]/Sqrt[r^2-x^2],x]
or equivalently
(3) Integrate[ x^2 ArcCosh[a/x]/Sqrt[r^2-x^2],x]
I have tried a lot of tricks (by part integration etc..) but I was not
able to find it.
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
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