$\quad \begin{aligned} h=\frac{2-1}{4} &=\frac{1}{4} \\ \text { Now, } x_{0} &=1, x_{1}=1+\frac{1}{4}, x_{2}=1+2 \times \frac{1}{4}, \\ x_{3} &=1+3 \times \frac{1}{4}, x_{4}=1+4 \times \frac{1}{4} \end{aligned}$
$$
\text { ie, } \begin{aligned}
x_{0} &=1, x_{1}=1.25, x_{2}=1.5, x_{3} \\
&=1.75, x_{4}=2 \\
\Rightarrow \quad y_{0} &=1, y_{1}=0.8, y_{2}=0.667, y_{3} \\
&=0.571, y_{4}=0.5
\end{aligned}
$$
$\therefore$ Using Simpson's $\frac{1}{3}$ rd rule
$$
\begin{aligned}
\int_{1}^{2} \frac{d x}{x}=& \frac{1}{12}[(1+0.5)+4(0.8+0.571)\\
&+2(0.667)] \\
=& \frac{1}{12}[1.5+5.484+1.334] \\
=& \frac{1}{12}[8.318]=0.6932
\end{aligned}
$$