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problem with Integrate



I have 3.0.0.0 for Windows. Consider the function:

In:    f[x_,b_] := x^2 b Exp[b x] / (1+ Exp[b x])^2  

We can correctly obtain the integral:

In:    Integrate[f[x,b],{x,0,Infinity},Assumptions->{b>0}] Out:  
Pi^2/6/b^2

However, using a particular value for the parameter:

In:    Integrate[f[x,Sqrt[3]],{x,0,Infinity}] Out:   0

I think that it is wrong, since

In:    Pi^2/6/b^2 /. b->Sqrt[3] //N
Out:   0.548311

In:    NIntegrate[f[x,Sqrt[3]],{x,0,Infinity}] Out:   0.548311

Finally, if we try the following, The system takes  a long time to
answer and I must abort the evaluation:

In:    Integrate[f[x,1.73],{x,0,Infinity}]

Apparently, the above behavior happens when the parameter  b is
substituted by expressions including square roots that  cannot be
simplified, and when the integration limit is Infinity.
 
Any suggestion will be greatly appreciated.

Alberto Ruiz



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