Đáp án: A
\(\displaystyle\int {f\left( x \right)dx} = \dfrac{{{7^x}}}{{\ln 7}}\left( {8x - 25 - \dfrac{8}{{\ln 7}}} \right) + C\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
F\left( x \right) = \displaystyle\int {f\left( x \right)} dx =\displaystyle \int {\left( {8x - 25} \right){{.7}^x}} dx\\
\left\{ \begin{array}{l}
u = 8x - 25\\
dv = {7^x}dx
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
du = 8dx\\
v = \dfrac{{{7^x}}}{{\ln 7}}
\end{array} \right.\\
\Rightarrow F\left( x \right) = \left( {8x - 25} \right).\dfrac{{{7^x}}}{{\ln 7}} - \displaystyle\int {\dfrac{{{{8.7}^x}}}{{\ln 7}}dx} \\
= \left( {8x - 25} \right).\dfrac{{{7^x}}}{{\ln 7}} - \dfrac{8}{{\ln 7}}.\displaystyle\int {{7^x}.dx} \\
= \left( {8x - 25} \right).\dfrac{{{7^x}}}{{\ln 7}} - \dfrac{8}{{\ln 7}}.\dfrac{{{7^x}}}{{\ln 7}} + C\\
= \dfrac{{{7^x}}}{{\ln 7}}\left( {8x - 25 - \dfrac{8}{{\ln 7}}} \right) + C
\end{array}\)
