Lim {{5^{2x}} - 6{e^{ -{x} / {2){d}}x} \] bằng:

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

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

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

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

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

Giải thích

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

\[ = \frac{{{{25}^x}}}{{\ln 25}} - 6\frac{{{{\rm{e}}^{ - \frac{x}{2}}}}}{{\ln {e^{ - \frac{1}{2}}}}} + C = \frac{{{{25}^x}}}{{2\ln 5}} + 12{{\rm{e}}^{ - \frac{x}{2}}} + C\].Chọn B.