\[\begin{array}{l}
 T2. \to \int {{x^n}} dx = \frac{{{x^{n + 1}}}}{{n + 1}} + C \\ 
 {\rm{Dokaz}}\,{\rm{(Proof):}} \\ 
 \int {{x^n}} dx = \left| {{x^n} = {e^{n\ln x}}} \right| = \int {{e^{n\ln x}}dx}  = \left| \begin{array}{l}
 n\ln x = t \\ 
 n\frac{{dx}}{x} = dt \\ 
 \ln x = \frac{t}{n} \to x = {e^{\frac{t}{n}}} \\ 
 \end{array} \right| = \int {{e^t}\frac{{{e^{\frac{t}{n}}}dt}}{n}}  = \frac{1}{n}\int {{e^{\frac{{t(n + 1)}}{n}}}dt}  = \left| \begin{array}{l}
 \frac{{t(n + 1)}}{n} = u \\ 
 \frac{{(n + 1)}}{n}dt = du \\ 
 dt = \frac{n}{{n + 1}}du \\ 
 \end{array} \right| = \frac{1}{n}\int {{e^u}\frac{n}{{n + 1}}du}  = \frac{1}{{n + 1}}{e^u} =  \\ 
  = \frac{1}{{n + 1}}{e^{\frac{{t(n + 1)}}{n}}} = \frac{1}{{n + 1}}{e^t}{e^{\frac{t}{n}}} = \frac{1}{{n + 1}}{e^{n\ln x}}x = \frac{1}{{n + 1}}{x^n}x = \frac{{{x^{n + 1}}}}{{n + 1}} \\ 
 \end{array}\]