Proof the convergence of this improper integral

Proof the convergence of this improper integral

I would like to prove $$\int_{1}^{\infty}\frac{\cos x}{x}dx$$ converges by
first establishing the convergence of the improper integral of
$$\int_{1}^{\infty} \frac{1}{x^{2}}dx$$The latter is easy but what is the
connection with the former? Thanks a lot!