When trying to find some solution to the double integral problem and poking around with Sage (4.7.2), I stumbled upon this behavior:
x,y,u,v,p,k=var('x,y,u,v,p,k')
integrate(x+y^k, y)
output (resembles maxima interaction):
Traceback (click to the left of this block for traceback)
...
Is k+1 zero or nonzero?
How can I answer to this (with nonzero)?