problem with Integrate
- To: mathgroup@smc.vnet.net
- Subject: [mg10368] problem with Integrate
- From: Alberto Ruiz <aruiz@dif.um.es>
- Date: Mon, 12 Jan 1998 04:10:02 -0500
- Organization: University of Murcia, Spain
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