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Mathematica 5.2 too slow...

Hi all,

I am evaluating this integral:

\!\(Integrate[\(\[ExponentialE]\^\(\[ImaginaryI]\ a\ z\)\ Sinh[z]\)\/\((b +
Cosh[z])\)\^2, {z, \(-?\), ?}, Assumptions \[Rule] \ {a > 0, b > 1}]\)

It needs 1 hour runing on my Pentium 4 3.2 GHZ 1GB memory desktop PC... 
anybody has some good ideas to improve?

Thanks a lot!

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