\[\begin{array}{l}
 T3. \to \int {{x^{ - 1}}} dx = \ln x + C \\ 
 {\rm{Dokaz}}\,{\rm{(Proof):}} \\ 
 \int {{x^{ - 1}}} dx = \left| {{x^{ - 1}} = {e^{ - \ln x}}} \right| = \int {{e^{ - \ln x}}dx}  = \left| \begin{array}{l}
  - \ln x = t \\ 
  - \frac{{dx}}{x} = dt \\ 
 dx =  - xdt =  - {e^{ - t}}dt \\ 
 \ln x =  - t \to x = {e^{ - t}} \\ 
 \end{array} \right| = \int {{e^t}( - {e^{ - t}})dt}  =  - \int {dt}  =  - t =  - ( - \ln x) = \ln x + C \\ 
 \end{array}\]