on sept 06, 09, Raymond Toy wrote
>>
>> Since maxima can find the indefinite integral, this
>> must be a limit(...) bug:
> Not necessarily. While I have not had a chance to look at the cause of
> the bug, the algorithm for definite integration is usually very, very
> different from the typical school method of finding the indefinite
> integral and plugging in the limits. Usually, maxima tries to convert
> the definite integral into some kind of contour integral and evaluates
> that via residues using precomputed results or by explicitly computing
> the residues.
>
> Ray
>
>
If we force use of the limit method, ldefint(..) also chokes in a different
way.
If we help it out by putting exp(-a*x) out front, it also gets "ind"
(%i1) display2d:false$
(%i2) assume( a>0, w>0 )$
(%i3) le : ldefint(x*exp(-a*x)*cos(w*x),x,0,inf);
(%o3) ('limit(w^3*x*%e^-(a*x)*sin(w*x)+a^2*w*x*%e^-(a*x)*sin(w*x)
+2*a*w*%e^-(a*x)*sin(w*x)
-a*w^2*x*%e^-(a*x)*cos(w*x)
-a^3*x*%e^-(a*x)*cos(w*x)
+w^2*%e^-(a*x)*cos(w*x)
-a^2*%e^-(a*x)*cos(w*x),x,inf))
/(w^4+2*a^2*w^2+a^4)
-w^2/(w^4+2*a^2*w^2+a^4)+a^2/(w^4+2*a^2*w^2+a^4)
(%i4) learg : part(le,1,1,1);
(%o4) w^3*x*%e^-(a*x)*sin(w*x)+a^2*w*x*%e^-(a*x)*sin(w*x)
+2*a*w*%e^-(a*x)*sin(w*x)
-a*w^2*x*%e^-(a*x)*cos(w*x)
-a^3*x*%e^-(a*x)*cos(w*x)+w^2*%e^-(a*x)*cos(w*x)
-a^2*%e^-(a*x)*cos(w*x)
(%i5) collectterms(learg,exp(-a*x));
(%o5) leart
(%i6) collectterms(learg,exp(-a*x));
(%o6) %e^-(a*x)*(w^3*x*sin(w*x)+a^2*w*x*sin(w*x)+2*a*w*sin(w*x)
-a*w^2*x*cos(w*x)-a^3*x*cos(w*x)+w^2*cos(w*x)
-a^2*cos(w*x))
(%i7) limit(%,x,inf);
(%o7) ind
Ted Woollett