![\bf u=\cfrac{1}{t}\implies t=\cfrac{1}{u}\implies t^2=\cfrac{1^2}{u^2}\implies t^2=\cfrac{1}{u^2}\\\\ -------------------------------\\\\ \displaystyle \int\limits_{1}^{e}u\cdot -\cfrac{1}{u^2}\cdot du\implies -1\int\limits_{1}^{e}\cfrac{1}{u}\cdot du\implies \left. -ln|u| \cfrac{}{}\right]_1^e](/tpl/images/0209/9451/76353.png)
![\bf \left. -ln\left( \frac{1}{t} \right) \cfrac{}{}\right]_1^e\implies \left[ -ln\left( \frac{1}{e} \right) \right]-\left[ -ln\left( \frac{1}{1} \right) \right]\implies \left[ -ln\left( e^{-1}\right) \right]-\left[ -ln\left( 1\right) \right] \\\\\\\ [-(-1)]-[-(0)]\implies 1-0\implies 1](/tpl/images/0209/9451/4d141.png)
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