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Câu hỏi: Cho hàm số $f\left( x \right)=2x+{{e}^{-x}}$. Tìm một nguyên hàm $F\left( x \right)$ của hàm số $f\left( x \right)$ thỏa mãn $F\left( 0 \right)=2023$
A. $F\left( x \right)={{x}^{2}}-{{e}^{-x}}+2023.$
B. $F\left( x \right)={{x}^{2}}-{{e}^{x}}+2024.$
C. $F\left( x \right)={{x}^{2}}+{{e}^{-x}}+2022.$
D. $F\left( x \right)={{x}^{2}}-{{e}^{-x}}+2024.$
A. $F\left( x \right)={{x}^{2}}-{{e}^{-x}}+2023.$
B. $F\left( x \right)={{x}^{2}}-{{e}^{x}}+2024.$
C. $F\left( x \right)={{x}^{2}}+{{e}^{-x}}+2022.$
D. $F\left( x \right)={{x}^{2}}-{{e}^{-x}}+2024.$
$F\left( x \right)=\int{\left( 2x+{{e}^{-x}} \right)dx}=\dfrac{2.{{x}^{2}}}{2}-{{e}^{-x}}+C={{x}^{2}}-{{e}^{-x}}+C$
$F\left( 0 \right)=2023\Leftrightarrow {{0}^{2}}-{{e}^{-0}}+C=2023\Leftrightarrow C=2024$
$F\left( x \right)={{x}^{2}}-{{e}^{-x}}+2024.$
$F\left( 0 \right)=2023\Leftrightarrow {{0}^{2}}-{{e}^{-0}}+C=2023\Leftrightarrow C=2024$
$F\left( x \right)={{x}^{2}}-{{e}^{-x}}+2024.$
Đáp án D.