Tìm: a) nguyên hàm (2^x + 3^x) ^ 2 b) nguyên hàm (e^x - e ^-x)^2

a) \(\int {{{\left( {{2^x} + {3^x}} \right)}^2}dx} \) = \(\int {\left( {{2^{2x}} + {{2.6}^x} + {3^{2x}}} \right)dx} \)

                            = \(\int {\left( {{4^x} + {{2.6}^x} + {9^x}} \right)} dx\)

                            = \(\int {{4^x}dx + \int {{{2.6}^x}dx + \int {{9^x}dx} } } \)

                            = \(\frac{{{4^x}}}{{\ln 4}} + \frac{{{{2.6}^x}}}{{\ln 6}} + \frac{{{9^x}}}{{\ln 9}}\)+ C.

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

                              = \(\int {{e^{2x}}dx + \int {{e^{ - 2x}}dx - \int {2dx} } } \)

                              = \(\frac{{{e^{2x}}}}{2} - \frac{{{e^{ - 2x}}}}{2} - 2x + C\).