I am looking for a value of an integral

[tex]\int^{\infty}_0 {r^{3-\epsilon} \over (r^2+N^2)^2}dr[/tex]

I have tried looking up a book by Gradshteyn and Ryzhik, however, its structure is quite complicated. Should I rewrite the integrand in some other non-obvious way to find it? Would you recommend using some other resource?

The answer is known (it involves Gamma functions), as the integral is a part of a paper about the "ABC theory" (toy QFT) by Kraus and Griffiths. However, I would like to 1) discover the optimal way to check complicated definite integrals in future and 2) check the value of this particular integral.

Thank you.