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Capability of Mathematica


Just wondering how well can Mathematica solve this equation I have before I
pay the price.
The equation goes as follow:

There are a total of 31 terms as illustrated above in 2 integrals over a
sphere like object.
Each of the term is like the following one:

Term 3 = a*b with,
a =
b =

So it's a really long doble integral of 31 terms, with a multiplication of 2
exponentials per term.  I can enter this in symbolic form, can't I?  How
fast and accurate will the solution be?  The answer will be numerical as
it's definite closed integral with specific limits.


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