Tính Lim {{3^{2x}} - 5{e^{ - \{x}/{2}{d}}x} bằng:

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\[\int {\left( {{3^{2x}} - 5{e^{ - \frac{x}{2}}}} \right){\rm{d}}x} \] bằng:

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

\[\frac{{{9^x}}}{{2\ln 3}} + 10{e^{ - \frac{x}{2}}} + C\].

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

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

Giải thích

Ta có \[\int {\left( {{3^{2x}} - 5{{\rm{e}}^{ - \frac{x}{2}}}} \right){\rm{d}}x} = \int {{9^x}{\rm{d}}x} + 10\int {{{\rm{e}}^{ - \frac{x}{2}}}d\left( { - \frac{x}{2}} \right)} = \frac{{{9^x}}}{{\ln 9}} + 10{{\rm{e}}^{ - \frac{x}{2}}} + C = \frac{{{9^x}}}{{2\ln 3}} + 10{{\rm{e}}^{ - \frac{x}{2}}} + C.\]

Chọn B.