Computing partial moments of the lomax distribution

Question

I have a variable that is distributed according to a lomax distribution (https://en.wikipedia.org/wiki/Lomax_distribution) with CDF and PDF given by

$F(x) = 1-\left(1+x\right)^{-\alpha}$

$f(x) = \alpha(1+x)^{-\alpha-1}$

I know that moments are given by

$\int_{0}^\infty x^n f(x) dx = \frac{\Gamma(\alpha-n)\Gamma(1+n)}{\Gamma(\alpha)}$

I want to compute partial moments of the form

$\int_{y}^\infty x^n f(x) dx$

but I am having trouble figuring out how to derive an expression for the partial moments. Can anyone give me a hint? Thanks!