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Câu hỏi: Biết $\int{f\left( x \right)}\text{ d}x=\dfrac{{{5}^{x}}}{\ln 5}+3x+C$, khi đó $f\left( x \right)$ bằng
A. $f\left( x \right)={{5}^{x}}+3$.
B. $f\left( x \right)=\dfrac{{{5}^{x}}}{\ln 5}+3x$.
C. $f\left( x \right)=\dfrac{{{5}^{x}}}{\ln 5}+3$.
D. $f\left( x \right)={{5}^{x}}+3x$.
A. $f\left( x \right)={{5}^{x}}+3$.
B. $f\left( x \right)=\dfrac{{{5}^{x}}}{\ln 5}+3x$.
C. $f\left( x \right)=\dfrac{{{5}^{x}}}{\ln 5}+3$.
D. $f\left( x \right)={{5}^{x}}+3x$.
Ta có $\int{f\left( x \right)}\text{ d}x=F\left( x \right)+C$ với ${F}'\left( x \right)=f\left( x \right)$.
Do đó $f\left( x \right)={{\left( \dfrac{{{5}^{x}}}{\ln 5}+3x \right)}^{\prime }}={{5}^{x}}+3$.
Do đó $f\left( x \right)={{\left( \dfrac{{{5}^{x}}}{\ln 5}+3x \right)}^{\prime }}={{5}^{x}}+3$.
Đáp án A.