I would like to get some advices or procedures on how to evaluate this three parametric integral:
$$\int_{0}^{+\infty}\dfrac{s^{\alpha}}{(1+s^2)(1+s)^{\beta}}\sin(k\,s)\;ds$$
$$(a\in\mathbb{Z}), \; (\beta\in\mathbb{Z},\; \beta>1), \;(k\in\mathbb{R},\; k\geq0).$$
It looks like that one can have an analytical result, I mean, in terms of the classical known functions.