How to make this integral (which does not converge) be finite?

[Emmanuel Ortiz]

I have to deal with this integral in my work, $$\int_{0}^{\infty} \frac{ k^4 e^{-2F^2k^2} }{ (k-k_0)^2 }dk$$ where $F^2>0 , k_0>0$ Is important to mention that it has a double pole in $k_0$ and as a consequence mathematically doesn’t converge. However I have seen before some methods in Quantum Field Theory to regularise divergent integrals with poles, unfortunally I have not had success in solving it. I’like to solve this integral in some reasonable way, perhaps with a physical argument, restrictions, approximation or under some assumptions. There exist a way to solve this Integral? Please help me.

 

[anorlunda]

Something must be missing. Which of those F, k, k0 things are functions of x?

 

[Emmanuel Ortiz]

Sorry is dk, I just corrected it