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symbolically solve an integral of ArcSinh[..]

  • To: mathgroup at
  • Subject: [mg7809] symbolically solve an integral of ArcSinh[..]
  • From: pknaus at (Patrick KNAUS)
  • Date: Sat, 12 Jul 1997 02:45:51 -0400
  • Organization: CERN, European Laboratory for Particle Physics
  • Sender: owner-wri-mathgroup at


could you please help me with the following problem:
I try to integrate symbolically

  Integrate[ArcSinh[(a-Sqrt[b^2-x^2])/(c-x)],x] where a,b,c=const

but don't obtain any solution using Mathematica 2.2 and 3.0. I tried some
equivalent formulations of the integrand like

  ArcSinh[z]=-I ArcSin[I z]

where z is the argument of ArcSinh in the integral: without success. Are
there any tricks you could suggest me to try out, any nice substitution?
I suspect the solution to contain some elliptic integrals.

best wishes,

From:   Patrick Knaus   
To: mathgroup at
        CERN, Division PS           Email: Patrick.Knaus at
        CH-1211 Geneva 23           Tel:   +41-22-767.2593

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