\[\begin{array}{l}
 T5. \to \int {{a^x}} dx = \frac{{{a^x}}}{{\ln a}} + C \\ 
 {\rm{Dokaz}}\,{\rm{(Proof):}} \\ 
 \int {{a^x}} dx = \left| \begin{array}{l}
 {a^x} = t \\ 
 {a^x}\ln adx = dt \\ 
 dx = \frac{{dt}}{{{a^x}\ln a}} = \frac{{dt}}{{t\ln a}} \\ 
 \end{array} \right| = \int {t\frac{{dt}}{{t\ln a}}}  = \frac{1}{{\ln a}}\int {dt}  = \frac{1}{{\ln a}} \cdot t = \frac{{{a^x}}}{{\ln a}} \\ 
 \end{array}\]