Peculiar behavior of Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg2617] Peculiar behavior of Integrate*From*: bruck at mtha.usc.edu (Ronald Bruck)*Date*: Thu, 30 Nov 1995 20:58:17 -0500

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