Question: Numerical integration over vectors (or analytic integration)

Is there a way in Maple to numerically integrate (with some symbolic variables retained), involving vectors?

Alternatively, is there a way to simply numerically integrate the following expression involving vectors, without any remaining symbolic variables remaining?

Integrate over vectors p1, p3
(with vector x remaining as free variable after integration)
( e^{-i p1 . x} (p1² + p3²) )  / ( (p3 - p1)² (p3²*a² +1)² )

If absolutely required for numerical integration, i.e. no other way to get maple to perform a semi-numerical integration, then vector x, and the scalar variable "a" can also be specified a value, but x should remain a vector. 

Of course, if the integration above can be done analytically, or even partly analytically (e.g. if the vectors are expressed in spherical polar co-ordinates, and some of the variables like Sin \theta etc. can be integrated over), that would be very useful as well.