I‘m calculating the determinants for applying the cramer's rule in Maple, however the result is very "large" and I can't see the pattern easily. For a general formula of the determinant please refer to this link: http://math.stackexchange.com/questions/193961/determinant-of-a-symmetric-matrix.

I wonder is there a way to simplify the answer to a nice symetrical form?

The pyramid is the standard simplex in 3D with vertices (0,0,0),(1,0,0),(0,1,0) and (0,0,1). Ie it's the convex hull of these 4 points. Because Maple does not have "convexhull" plot command for 3D objects, so instead one has to plot a pyramid.

My commands:

                            with(plots);

 ...

I want to calculate above integral in Maple15,  the parameters n_1, n_2 and n_3 are all positive integers.
I tried to input the following command: int(int((1-x)*(1-y)(x+y)*(x^n_1)*(y^n_2)*(1-x-y)^n_3, y=0..1-x),x=0..1);

After I pressed enter it then appeared an error message: "Error, unable to match delimiters"