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Câu hỏi: Cho $F\left( x \right)=\int{x{{e}^{x}}dx}$. Khi đó, $F\left( x \right)$ bằng
A. $x{{e}^{x}}+{{e}^{x}}+C$
B. $-x{{e}^{x}}+{{e}^{x}}+C$
C. $x{{e}^{x}}-2{{e}^{x}}+C$
D. $x{{e}^{x}}-{{e}^{x}}+C$
A. $x{{e}^{x}}+{{e}^{x}}+C$
B. $-x{{e}^{x}}+{{e}^{x}}+C$
C. $x{{e}^{x}}-2{{e}^{x}}+C$
D. $x{{e}^{x}}-{{e}^{x}}+C$
Đặt $\left\{ \begin{aligned}
& u=x \\
& dv={{e}^{x}}dx \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& du=dx \\
& v={{e}^{x}} \\
\end{aligned} \right.$
$F\left( x \right)=\int{x{{e}^{x}}dx=x{{e}^{x}}-\int{{{e}^{x}}dx=x{{e}^{x}}-{{e}^{x}}+C}}$
& u=x \\
& dv={{e}^{x}}dx \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& du=dx \\
& v={{e}^{x}} \\
\end{aligned} \right.$
$F\left( x \right)=\int{x{{e}^{x}}dx=x{{e}^{x}}-\int{{{e}^{x}}dx=x{{e}^{x}}-{{e}^{x}}+C}}$
Đáp án D.