#2246 integrate problems

[Aleksas]

(%i1) integrate(log(cos(x)),x,0,%pi/2);
defint: integral is divergent.
-- an error. To debug this try: debugmode(true);
The result should be -1/2*%pi*log(2)

(%i2) integrate(log(2*cos(x)),x,0,%pi/2);
defint: integral is divergent.
-- an error. To debug this try: debugmode(true);
The result should be 0

(%i3) integrate(log(sin(2*x)),x,0,%pi/2);
defint: integral is divergent.
-- an error. To debug this try: debugmode(true);
The result should be -1/2*%pi*log(2)

(%i4) integrate(log(sin(x)),x,0,%pi/2);
(%o4) integrate(log(sin(x)),x,0,%pi/2)
The result should be -1/2*%pi*log(2)

(%i5) integrate(x*cot(x),x,0,%pi/2);
(%o5) integrate(x*cot(x),x,0,%pi/2)
The result should be 1/2*%pi*log(2)

(%i6) integrate(x^2/sin(x)^2,x,0,%pi/2);
(%o6) integrate(x^2/sin(x)^2,x,0,%pi/2)
The result should be %pi*log(2)

(%i7) integrate(asin(x)/x,x,0,1);
(%o7) integrate(asin(x)/x,x,0,1)
The result should be 1/2*%pi*log(2)

(%i8) build_info()$
Maxima version: 5.25.0
Maxima build date: 12:0 8/2/2011
Host type: i686-pc-mingw32
Lisp implementation type: Clozure Common Lisp
Lisp implementation version: Version 1.7-r14925M (WindowsX8632)

[Robert Dodier]

For the record, there has been a commit which is a partial fix for this bug (see commit 883dc43328380), although the results are still problematic. There are repeated questions of the form "Is %pi/4 an integer?" "Is 2*%pi an integer?" etc. and the results are different from what's shown in the bug report. Also integrate(log(sin(2*x)),x,0,%pi/2) appears to cause Maxima to run forever and eventually use up all of free memory.

[David Scherfgen]

All except (%i6) and (%i7) are fixed in current Maxima.