Bug introduced in 8.0.0 and fixed in 9.0.0
Consider the following:
regFunc[x_,y_]:=Boole[-5<4x+3y<5 && -2<3x+2y<2];
Integrate[regFunc[x,y]*((4x+3y)(3x+2y))^4,{x,-100,100},{y,-100,100}]//N
Integrate[regFunc[x,y]*(12x^2+17x*y+6y^2)^4,{x,-100,100},{y,-100,100}]//N
In the first example, Mathematica seems to figure out the correct substitution, and arrives at 16000, which is the correct answer. In the second integration, (integrating the same expression, but expanded), Mathematica gives 5885078144/382725, which is 15376.8. This is clearly a bug, is this well-known?
I am using Mathematica 8.04, 64bit Linux.
EDIT: I got an email from the tech support, and I took the answer as a confirmed bug.
xy
in the second example? (guess not) $\endgroup$