Peculiar behavior of Integrate

• Subject: [mg2617] Peculiar behavior of Integrate
• From: bruck at mtha.usc.edu (Ronald Bruck)
• Date: Thu, 30 Nov 1995 20:58:17 -0500
• Approved: usenet@wri.com
• Distribution: local
• Newsgroups: wri.mathgroup
• Organization: Wolfram Research, Inc.

```Can anyone explain this to me?  This comes from Problem G.1.b.iii of problem
set 2.03 of Davis, Porta and Uhl's Calculus and Mathematica:

If I execute

Clear[t,T]
100 + Integrate[(160 E^t)/(0.5 + E^t)^2,{t,0,T}]
%/.T->2400

Mathematica does it in a wink.  If I execute

Clear[t,T]
100 + Integrate[(160 E^t)/(1/2 + E^t)^2,{t,0,2400}]

Mathematica does it quick as a wink.  (This is on a Power Mac 9500/132;
your winks may vary.)

But if I execute

Clear[t,T]
100 + Integrate[(160 E^t)/(0.5 + E^t)^2,{t,0,2400}]

then Mathematica grinds away... and grinds away... and so far I haven't had
the patience to outwait it.  When I interrupt the kernel it takes almost a
minute to back out of whatever it's doing.

What's it doing?  Is this some local user-preference which is causing this?
Can anyone verify similar behavior on other platforms?

This is Mathematica 2.2.2.1 for the Power Macintosh (the printing-magnifi-
cation-but-fix version).

I asked the student whether she had made the proper propitiary sacrifices
before sitting down at the computer, and she swore she had ;-)

--Ron Bruck

```

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