\[\int {\left( {{5^{2x}} - 6{e^{ - \frac{x}{2}}}} \right){\rm{d}}x} \] bằng

21/50

\[{e^x} - \frac{1}{2}{e^{ - 2x}} + C\].

\[\frac{{{{25}^x}}}{{2\ln 5}} + 12{e^{ - \frac{x}{2}}} + C\].

\[{e^x} - 2{e^{ - 2x}} + C\].

\[\frac{{{e^{x + 1}}}}{{x + 1}} + \frac{{{e^{ - 2x + 1}}}}{{ - 2x + 1}} + C\].

Giải thích

Ta có \[\int {\left( {{5^{2x}} - 6{e^{ - \frac{x}{2}}}} \right){\rm{d}}x} = \int {{5^{2x}}{\rm{d}}x} - 6\int {{e^{ - \frac{x}{2}}}} {\rm{d}}x = \int {{{25}^x}} {\rm{d}}x - 6\int {{{\left( {{e^{ - \frac{1}{2}}}} \right)}^x}{\rm{d}}x} \]

\( = \frac{{{{25}^x}}}{{\ln 25}} - 6 \cdot \frac{{{{\left( {{e^{ - \frac{1}{2}}}} \right)}^x}}}{{\ln {e^{ - \frac{1}{2}}}}} + C = \frac{{{{25}^x}}}{{\ln 25}} + 12{e^{ - \frac{x}{2}}} + C\). Chọn B.