Changing to Polar coordinates in order to calculate this integral

[Replusz]

TL;DR

I am a bit lost regarding what happens here.
the k^2+m^2 part stays there.
What happens to the exp? and to the d^3k ?

Thank you!

m a

 

[Gaussian97]

Try to write 3.66 in spherical coordinates, and perform the integrals of $\phi$ and $\theta$.

 

[Replusz]

I get a part where I have to integrate (cos(kr*cos(theta))+i*sin(kr*cos(theta)))*sin(theta) dtheta
Which seems terrible

 

[Replusz]

OK with the help of wolframalpha I convinced myself that this is indeed what we want.
(imaginary part is 0, real part gives 3.67)

Thank you Gaussian97! :)