calculus - does the integral $int _{1}^{infty }!{frac {sin left( cos left( x right) +sin left( xsqrt {3} right) right) }{x}}{dx}$ converges?

I want to know if this integral converges or not : $\int _{1}^{\infty }\!{\frac {\sin \left( \cos \left( x \right) +\sin\left( x\sqrt {3} \right) \right) }{x}}{dx}.$ I tried to integrate by parts or to use dirichlet's test, but it seems impossible to prove that $\int _{1}^{x}\!\sin \left( \cos \left( t \right) +\sin \left( t\sqrt {3} \right) \right) {dt}$ is bounded. Do you have any idea how to solve this problem?