Everybody,

I am trying to make my way on the Mathematica learning curve and am testing some integrals that I know how to solve.

This is a case of an integral over two orbital-like functions (never mind if you are not familiar with them). My function is:

Simplify[(x - x1) (y - y2) Exp[-alpha ((x - x1)^2 + (y - y1)^2 + (z - z1)^2)] Exp[-alpha ((x - x2)^2 + (y - y2)^2 + (z - z2)^2)]]

x, y and z are real variables, so I put:

Element[{x, y, z}, Reals]

x1,x2,y1,y2,z1,z2 are constants and real, so:

Element[{x1, y1, z1, x2, y2, z2}, {Constants, Reals}]

alpha is also a constant:

Element[{alpha}, {Constants, Reals, Positive}]

(I am not sure about the statement Positive)

I then integrate by:

Integrate[(x - x1) (y - y2) Exp[- alpha ((x - x1)^2 + (y - y1)^2 + (z - z1)^2)] Exp[-alpha ((x - x2)^2 + (y - y2)^2 + (z - z2)^2)], {x, -Infinity, +Infinity}, {y, -Infinity, +Infinity}, {z, -Infinity, +Infinity}, Assumptions -> alpha > 0]

and basically my problem is that it takes so long to evaluate this. The end answer is correct but I am just wondering if I did something pretty stupid. Would it have been better to put the assumptions inside the Integrate block or something alike ?

Thanks,

Patrick