[Maxima-bugs] [ maxima-Bugs-2977217 ] maxima can not integrate x*exp(-1/2*(x-m)^2)

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Bugs item #2977217, was opened at 2010-03-26 18:58
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Nobody/Anonymous (nobody)
Assigned to: Nobody/Anonymous (nobody)
Summary: maxima can not integrate x*exp(-1/2*(x-m)^2)

Initial Comment:
Maxima can not integrate the function x*exp(-1/2*(x-m)^2)

Maxima 5.20.1 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) integrate(x*exp(-1/2*(x-m)^2),x);
                                                               2
                                                        (x - m)
                                                /     - --------
                                                [          2
(%o1)                                           I x %e           dx
                                                ]
                                                /

The correct solution would be

(%i2) diff(-exp(-1/2*x^2+m*x-1/2*m^2)+1/2*m*sqrt(%pi)*sqrt(2)*erf(1/2*sqrt(2)*x-1/2*m*sqrt(2)),x);
                                                                        2          2
                                        x         m    2               x          m
                                  - (------- - -------)              - -- + m x - --
                                     sqrt(2)   sqrt(2)                 2          2
(%o2)                         m %e                       - (m - x) %e

----------------------------------------------------------------------

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