Some of this seems to be triggered by the subscripts. For example:

(%i19) integrate(exp(-u^2*((x11-x21)^2+(x12-x22)^2+(x13-x23)^2)), u, -inf, inf); 2 2 2 2 2 2 Is x23 - 2 x13 x23 + x22 - 2 x12 x22 + x21 - 2 x11 x21 + x13 + x12 + x11 positive, negative or zero? pos; inf / 2 2 2 2 [ - u ((x13 - x23) + (x12 - x22) + (x11 - x21) ) (%o19) I %e du ] / - inf

With subscripts, you get a confusing looking question with sine, cosine, atan2 and abs! (Presumably the result of realpart or imagpart at some point)

However, it's a little unfortunate that we get asked for a sign at all. I guess that the exponent gets expanded at some point before the sign gets asked. Since the resulting noun form isn't expanded, we presumably gave up on that line of questioning...

Also,

(%i22) integrate(exp(-u^2 * a), u, -inf, inf); Is a positive, negative or zero? pos; sqrt(%pi) (%o22) --------- sqrt(a)

which is good. I wonder why the example above gives a noun form instead.