real analysis - An improper integral that diverges

I want to show that the integral

\begin{align*}
\int_1^{\infty} \frac{|\sin x|}{x} \text{ d}x
\end{align*}
diverges without sketching the function and obtain the divergence of the integral geometrically. I wonder if the comparison test works here.

I appreciate any help. Thanks.

Answer

Hint: Also used in this answer:
$$
\begin{align}

\int_{k\pi}^{(k+1)\pi}\frac{|\sin(x)\,|}x\,\mathrm{d}x
&\ge\frac1{(k+1)\pi}\int_{k\pi}^{(k+1)\pi}|\sin(x)\,|\,\mathrm{d}x\\
&=\frac2{(k+1)\pi}
\end{align}
$$