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These are questions asked by Arny

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 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. 


In Maple 17, the following expression needs to be integrated with respect to q3, p3 and q. Here, mu is a real, positive scalar. 

a := 1/(sqrt(mu^2+(px-p3x-q3x)^2)*sqrt(mu^2+(-p3x+qx-q3x)^2)*sqrt(mu^2+q3x^2)*(sqrt(mu^2+(-p3x+qx-q3x)^2)+sqrt(mu^2+q3x^2)))

However, the integration will not work with the "int" command (e.g. wrt q3). The indefinite integration will work if the integral is evaluated using the steps: highlight expression -> right click -> Integrate -> wrt q3 command.

The output of the integral (using the above method) is very long, it's impossible to manipulate the answer (on my i5, 8GB machine running Maple 17) because it is very tough to copy such a long output. Also, there is no way to specify that mu is a positive scalar. 

Is there a better way to perform the integration, e.g. between 0 and lambda, -1 through 1, or -infinity to +infinity?  


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