challenging integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg12729] challenging integration*From*: quartier at umnw.ethz.ch (Robin Quartier)*Date*: Thu, 4 Jun 1998 02:52:14 -0400*Organization*: Swiss Federal Institute of Technology (ETHZ)*Sender*: owner-wri-mathgroup at wolfram.com

Greetings! I have some problems with the calculation of the entropy rank of the following distribution: epsilon[x_]:=a*b/(b^2 - a^2)*(b*Exp[-a*x] - a*Exp[-b*x]) with a and b >0 As you can see, there is a kind of symmetry between the parameters: you can change a for b and b for a without changing the expression. I can not get an answer for this: Integrate[epsilon[x]*Log[epsilon[x]],{x,0,Infinity}] (Mathematica re-prints the input) Does anybody have an idea? Is this possible to integer analytically? What could I possibly do wrong? Best regards Robin Quartier