In preparing a demonstration of the Arithmetic Geometric Mean for students, I came across the following behaviour, in which the second symbolic integral (or its numerical evaluation) are wrong. All numerical values should have been the same:
It is corrected with Maple 6. (U. Klein)
You can avoid this bug in the following way:
It works for both problems:
This looks more complicated.
You get a small imaginary value,which must be due to rounding errors, so you can neglect it.
It is interesting that this works correctly in release 4: