#2501 %pi/8 is definitely not an integer

[kcrisman]

(%i5) display2d:false;

Probably it shouldn't be asked that these are integers.

(%o5) false
(%i6) integrate(log(cot(x)-1),x,0,%pi/4);

Is %pi/8 an ?integer?

n;
Is %pi/4 an ?integer?

n;
Is 2*%pi an ?integer?

n;
(%o6) -(%i(2li2-2li2)+%pilog(2))/4
+%ili2/2-%ili2/2

[kcrisman]

Ted Woollett has a very similar example, though without the polylogs, at http://www.math.utexas.edu/pipermail/maxima/2012/030780.html

(%i22) integrate(log(cos(x)),x,0,%pi/2);
Is %pi/2 an ?integer?

n;
Is %pi/4 an ?integer?

n;
Is 2*%pi an ?integer?

n;
Is 4*%pi an ?integer?

n;
(%o22) %i%pi^2/24-(6%pilog(4)+%i%pi^2)/24

(%i23) ratsimp(%);
(%o23) -%pi*log(4)/4

(%i24) float(%);
(%o24) -1.088793045151801

(%i25) quad(log(cos(x)),x,0,%pi/2);
(%o25) -1.088793045151803

[Barton Willis]

The function nonintegerp (defined in compar.lisp) is the culprit:

(%i20) ?nonintegerp(%pi/8);
(%o20) false

[Barton Willis]

Fixed by commit 2558370d67e97e9d597c2289a25199f74cf7487d