Would the following series be conditionally convergent, absolutely convergent or divergent?
$$\sum^\infty_{k=1}\frac{k\sin{(1+k^3)}}{k+\ln{k}}$$
Whereas for sine functions in series like this, you can usually say that it just alternates between 1 and -1 but would this one do the same for $k\geq1$? I don't think it would so that would mean I can't use the alternating series test. Perhaps, then, the ratio test or some comparison test?