If $f(x)\nearrow\infty$ in $[a, \infty)$ and $f'(x)$ is continuous in $[a, \infty)$ then $\int_{a}^{\infty}\frac{f'(x)}{f(x)}\sin(f(x))$ converges
I'm not exactly sure what to try here. I thought of Dirichlets test but I can't seem to identify the right functions to make it work.