A simple integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg47596] A simple integral*From*: "Dr A.H. Harker" <a.harker at ucl.ac.uk>*Date*: Sat, 17 Apr 2004 02:31:37 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

A simple integration, under Version 4.1.2: Integrate[x^2 Exp[-(x-$B&L(B)^2/(2 $B&R(B^2)],{x,-$B!g(B,$B!g(B}] 2 If[Re[$B&R(B ] > 0, 2 Sqrt[2 Pi] Sqrt[$B&R(B ] 2 2 ($B&L(B + $B&R(B ), 2 x Integrate[----------------, 2 2 (x - $B&L(B) /(2 $B&R(B ) E {x, -Infinity, Infinity}]] and the same under 5.0 Integrate[x^2 Exp[-(x-$B&L(B)^2/(2 $B&R(B^2)],{x,-$B!g(B,$B!g(B}] 2 $B&L(B If[Re[$B&R(B ] > 0 && Re[--] < 0, 2 $B&R(B 2 2 Sqrt[2 Pi] $B&L(B ($B&L(B + $B&R(B ) -(----------------------), 2 $B&L(B Sqrt[--] 2 $B&R(B 2 x Integrate[----------------, 2 2 (x - $B&L(B) /(2 $B&R(B ) E {x, -Infinity, Infinity}, Assumptions -> $B&L(B 2 Re[--] >= 0 || Re[$B&R(B ] <= 0 2 $B&R(B ]] Two questions: 1. Whence the extra condition in Version 5? 2. Why the negative sign in Version 5? Using PowerExpand then gives a negative result for this integral which is patently, for real parameters, positive. Am I alone in feeling that Version 5 has introduced more problems than it has solved? Dr A.H. Harker Department of Physics and Astronomy University College London Gower Street LONDON WC1E 6BT (44)(0)207 679 3404 a.harker at ucl.ac.uk

**Follow-Ups**:**Re: A simple integral***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>