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challenging integration


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


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