Triplequad for solving integral

I'm attempting to solve the integral: ∭D dxdydz/(x+y+z+1)^3 where D: x>0,y>0,z>0,x+y+z<2

, specifically with the use of the triplequad command. I'm having trouble determining the constant limits so I wonder if there is a way to allow for triplequad to use bounds that depend upon variables?

If not, is there anyone who happens to be able to determine the constant limits for me :)?

Thanks in advance!

[Roger Stafford]

The region of integration in your problem is such that you cannot use constant limits of integration with the triple integral in its present form. You would have to make a change of variables to be able to do that.

Answer 1

[Roger Stafford]

I don't believe the 'triplequad' function will accept limits that depend on variables. However the function 'integral3' does accept variable limits for two of its limits. See its documentation at:

 http://www.mathworks.com/help/matlab/ref/integral3.html

Your particular integral is sufficiently simple that you could find its precise value using elementary calculus or the 'int' function in the Symbolic Toolbox instead of using numerical approximations.