Am Sonntag, den 30.08.2009, 23:56 -0300 schrieb Alejandro Jakubi:
> I have been browsing recent posts to this list and one of them was about the
> following integral:
>
> integrate(x*log(sin(x)),x,0,%pi);
>
> and a long result was shown. I have tried it with Maxima 5.19.1, but got
> instead an error message:
>
> Maxima encountered a Lisp error:
> Error in PROGN [or a callee]: Bind stack overflow.
> Automatically continuing.
> To reenable the Lisp debugger set *debugger-hook* to nil.
>
>
> It sounds like a bug.
The bug has been fixed in Maxima 5.19.2 and Maxima 5.19post.
Unfortunately, Maxima 5.19.1 has shown this bug the first time.
This is the new result:
(%i5) integrate(x*log(sin(x)),x,0,%pi);
(%o5) %i*(('limit(12*'imagpart(li[3](%e^(%i*x)))
-12*x*'realpart(li[2](%e^(%i*x)))
+12*'imagpart(li[3](-%e^(%i*x)))
-12*x*'realpart(li[2](-%e^(%i*x)))
+6*x^2*atan(sin(x)/(cos(x)+1))
+6*x^2*atan(sin(x)/(cos(x)-1))-2*x^3,x,0,plus))
/12
-('limit(12*'imagpart(li[3](%e^(%i*x)))
-12*x*'realpart(li[2](%e^(%i*x)))
+12*'imagpart(li[3](-%e^(%i*x)))
-12*x*'realpart(li[2](-%e^(%i*x)))
+6*x^2*atan(sin(x)/(cos(x)+1))
+6*x^2*atan(sin(x)/(cos(x)-1))-2*x^3,x,%pi,minus))
/12)
-%pi*'imagpart(%pi^2/6)-%pi*'imagpart(-%pi^2/12)-%pi^2*log(4)/4
We have to evaluate the result of the integral to times to get a
simplified and correct answer. This is an open bug:
(%i6) %,nouns;
(%o6) %i*((12*'imagpart(zeta(3))+12*'imagpart(-3*zeta(3)/4))/12
-(12*'imagpart(zeta(3))+12*'imagpart(-3*zeta(3)/4)
-12*%pi*'realpart(%pi^2/6)
-12*%pi*'realpart(-%pi^2/12)+%pi^3)
/12)
-%pi^2*log(4)/4
(%i7) %,nouns;
(%o7) -%pi^2*log(4)/4
Dieter Kaiser