Tìm: a) nguyên hàm (2^x + 1 / 3^x); b) nguyên hàm (x^2 + 2^x)

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

                              = \(\int {2{e^x}dx + \int {{3^{ - x}}dx} } \)

                              = 2ex − \(\frac{1}{{{3^x}.\ln 3}}\) + C.

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

                           = \(\frac{{{x^3}}}{3} + \frac{{{2^x}}}{{\ln 2}} + C\).