∫ e e 4 d x x l n x {\displaystyle \int _{e}^{e^{4}}{\frac {dx}{x{\sqrt {lnx}}}}} = ∫ 1 4 1 u d u {\displaystyle \int _{1}^{4}{\frac {1}{u}}du} = ∫ 1 4 u − 1 / 2 d u {\displaystyle \int _{1}^{4}u^{-1/2}du} = u 1 / 2 1 / 2 | 1 4 {\displaystyle {\frac {u^{1/2}{1/2}}{\bigg |}}_{1}^{4}} = 2 u 1 / 2 | 1 4 {\displaystyle {2u}^{1/2}{\bigg |}_{1}^{4}}
