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I want to calculate an integral of the form

[tex] \int d \vec k f(\vec k \cdot \vec x) g(k^2) \vec k, [/tex]

where k and x are 3-dimensional vectors and integration spans the whole 3D volume. I wonder what is the

general approach to the problem? Were it not for the vector k term in the integral, one could just switch to

the spherical coordinates and perform integration over two variables (|k| and one of the angles, while the other

angle gives just a constant factor). But now it is not clear how to do that, since the result of the integration

is supposed to be a 3-vector itself.

Any suggestions or references are welcome.

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# Multiple integral over a function of a vector

Can you offer guidance or do you also need help?

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