The integrate function returns an unevaluated limit
Subject: The integrate function returns an unevaluated limit
From: Anton Voropaev
Date: Fri, 31 Dec 2010 20:40:30 +0300
integrate(%e^(-a*r)*log(r),r,0,inf) assuming a>0
is not evaluated in Maxima directly.
One can help by making the change s=a*r
and expanding the integrand.
Even so, can we do something with the limit?
INPUT
display2d : false$
build_info()$
assume(a>0)$
I1 : 'integrate(%e^(-a*r)*log(r),r,0,inf);
I1, nouns;
I2 : changevar(I1,s-a*r,s,r);
I2, nouns;
I3 : expand(I2);
I3, nouns;
INPUT AND OUTPUT
(%i1) display2d : false$
(%i2) build_info()$
Maxima version: 5.22.1
Maxima build date: 11:48 8/13/2010
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8
(%i3) assume(a>0)$
(%i4) I1 : 'integrate(%e^(-a*r)*log(r),r,0,inf);
(%o4) 'integrate(%e^-(a*r)*log(r),r,0,inf)
(%i5) I1, nouns;
(%o5) -'limit(-%e^-(a*r)*log(r)/a-gamma_incomplete(0,a*r)/a,r,0,plus)
(%i6) I2 : changevar(I1,s-a*r,s,r);
(%o6) ('integrate(%e^-s*(log(s)-log(a)),s,0,inf))/a
(%i7) I2, nouns;
(%o7) -('limit(-%e^-s*log(s)+log(a)*%e^-s-gamma_incomplete(0,s),s,0,plus))/a
(%i8) I3 : expand(I2);
(%o8) ('integrate(%e^-s*log(s)-log(a)*%e^-s,s,0,inf))/a
(%i9) I3, nouns;
(%o9) (-log(a)-%gamma)/a