tính tích phân 5^2x - 6e^ - x/2 dx bằng:

16/40

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

Chọn B

Ta có \[\int {\left( {{5^{2x}} - 6{{\rm{e}}^{ - \frac{x}{2}}}} \right){\rm{d}}x} = \int {{{25}^x}{\rm{d}}x} + 12\int {{{\rm{e}}^{ - \frac{x}{2}}}d\left( { - \frac{x}{2}} \right)} = \frac{{{{25}^x}}}{{\ln 25}} + 12{{\rm{e}}^{ - \frac{x}{2}}} + C = \frac{{{{25}^x}}}{{2\ln 5}} + 12{{\rm{e}}^{ - \frac{x}{2}}} + C\].