Tính các tích phân sau: a) tích phân 0 1 (3^x - 2e^x) dx; b)tích phân (e^x - 1) ^ 2 / 2e^x

a) \(\int\limits_0^1 {\left( {{3^x} - 2{e^x}} \right)dx} \) = \(\int\limits_0^1 {{3^x}dx}  - \int\limits_0^1 {2{e^x}dx} \)

                             = \(\left. {\frac{{{3^x}}}{{\ln 3}}} \right|_0^1 - \left. {2{e^x}} \right|_0^1\)

                             = \(\frac{2}{{\ln 3}} - 2e + 2\).

b) \(\int\limits_0^1 {\frac{{{{\left( {{e^x} - 1} \right)}^2}}}{{2{e^x}}}} dx\) = \(\int\limits_0^1 {\frac{{{e^{2x}} - 2{e^x} + 1}}{{2{e^x}}}dx} \)

                          = \(\frac{1}{2}\int\limits_0^1 {\left( {{e^x} - 2 + {e^{ - x}}} \right)dx} \)

                          = \(\left. {\frac{1}{2}\left( {{e^x} - 2x - {e^{ - x}}} \right)} \right|_0^1\)

                          =  \(\frac{{e - 2 - {e^{ - 1}}}}{2}\).