Is there a way in SymPy to either analytically integrate, or numerically 
integrate (with some symbolic variables retained), involving vectors?


Integrate over vectors *p1*, *p3*
( e-i *p1 . x* (*p1*2 + *p3*2) )  / ( (*p3* - *p1*)2 (*p3*2a2 +1)2 )


*(with vector x , and scalar "a" remaining as free variables after 
integration)*


If absolutely required for numerical integration, i.e. no other way to get 
SymPy 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 attempted analytically if 
possible in SymPy, 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), any suggestions towards such an 
approach would be very useful as well. 

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