MathGroup Archive 1998

[Date Index] [Thread Index] [Author Index]

Search the Archive

problem with Integrate

I have 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:  

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

  • Prev by Date: Re: Easy question: Infinite Series, Infinite Sequences
  • Next by Date: Re: curve fitting
  • Prev by thread: permutation groups
  • Next by thread: Re: problem with Integrate