Convergence (absolutely) of an improper integral $\int_{-\infty}^\infty\frac{\sin(\sin x)}{1+\log(\lfloor|x|\rfloor! + 2)} dx$

Question

$$\int_{-\infty}^\infty\frac{\sin(\sin x)}{1+\log(\lfloor|x|\rfloor! + 2)} dx$$

I need to check if this integral is absolutely convergent... I've shown it's convergent (not absolutely), according dirichlet test. I think it's conditionally convergent, but I don't know how to prove it.

Thank you