∫ 1 9 1 2 x d x = 1 2 ∫ 1 9 1 x d x = 1 2 ln | x | | 1 9 {\displaystyle {\begin{aligned}\int _{1}^{9}{\frac {1}{2x}}dx={\frac {1}{2}}\int _{1}^{9}{\frac {1}{x}}dx={\frac {1}{2}}\ln {|x|}{\bigg |}_{1}^{9}\end{aligned}}}