> integrate(integrate(1/16,y,-2,(z+2*x+4)/(x+2)),x,(-z-8)/4,2)

Seems to work for me:

----------------------------------------------------------------------
| Sage Version 4.6.1, Release Date: 2011-01-11                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: var("x y z")
(x, y, z)
sage: integrate(integrate(1/16,y,-2,(z+2*x+4)/(x+2)),x,(-z-8)/4,2)
[...]
TypeError: Computation failed since Maxima requested additional
constraints (try the command 'assume(z+16>0)' before integral or limit
evaluation, for example):
Is  z+16  positive, negative, or zero?
sage: assume(z+16>0)
sage: integrate(integrate(1/16,y,-2,(z+2*x+4)/(x+2)),x,(-z-8)/4,2)
[...]
TypeError: Computation failed since Maxima requested additional
constraints (try the command 'assume(z>0)' before integral or limit
evaluation, for example):
Is  z  positive, negative, or zero?
sage: assume(z<0)
sage: integrate(integrate(1/16,y,-2,(z+2*x+4)/(x+2)),x,(-z-8)/4,2)
-1/16*z*log(-1/4*z) + 1/16*z*log(4) + 1/16*z + 1

What version of Sage are you running?  (Note that 4.6.2 has just been released.)


Doug

--
Department of Earth Sciences
University of Hong Kong

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