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