a) \(\int\limits_0^1 {{3^x}dx} = \frac{{{3^x}}}{{\ln 3}}\left| {\begin{array}{*{20}{c}}{^1}\\{_0}\end{array}} \right. = \frac{{{3^1}}}{{\ln 3}} - \frac{{{3^0}}}{{\ln 3}} = \frac{2}{{\ln 3}}\)
b) \(\int\limits_0^1 {({{2.3}^x} - 5{e^x})dx} = \int\limits_0^1 {{{2.3}^x}dx} - \int\limits_0^1 {5{e^x}dx} \)
\( = 2\int\limits_0^1 {{3^x}dx} - 5\int\limits_0^1 {{e^x}dx} = \frac{{{{2.3}^x}}}{{\ln 3}}\left| {\begin{array}{*{20}{c}}{^1}\\{_0}\end{array}} \right. - 5{e^x}\left| {\begin{array}{*{20}{c}}{^1}\\{_0}\end{array}} \right.\)
\( = \left( {\frac{{{{2.3}^1}}}{{\ln 3}} - \frac{{{{2.3}^0}}}{{\ln 3}}} \right) - \left( {5{e^1} - 5{e^0}} \right) = \frac{4}{{\ln 3}} - 5e + 5\).