Q.Evaluate $\displaystyle\int_{1}^{3} \frac{1}{x}\,dx$.

The antiderivative of $\tfrac1x$ is $\log|x|$; evaluate from $1$ to $3$.

This is the reciprocal case (§2), with antiderivative $\log|x|$.

Evaluate at the limits. On $[1,3]$, $x > 0$, so

Numerically $\log 3 \approx 1.0986$ (natural logarithm). …

By the log law directly: $\displaystyle\int_1^3\tfrac1x,dx = …

Do not misapply the power rule to $\tfrac1x$ — its antiderivative is $\log|x|$, not $\tfrac{x^0}{0}$ (which is undefined). And …