# Question:Numerical integration over vectors (or analytic integration)

## Question:Numerical integration over vectors (or analytic integration)

Maple

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.

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