Google
Câu hỏi: $\int{{{x}^{2}}{{\text{e}}^{x}}\text{d}x}$ bằng
A. ${{x}^{2}}{{\text{e}}^{x}}-2\int{x{{\text{e}}^{x}}\text{d}x}$.
B. ${{x}^{2}}{{\text{e}}^{x}}+2\int{x{{\text{e}}^{x}}\text{d}x}$.
C. ${{x}^{2}}{{\text{e}}^{x}}-\int{x{{\text{e}}^{x}}\text{d}x}$.
D. ${{x}^{2}}{{\text{e}}^{x}}+\int{x{{\text{e}}^{x}}\text{d}x}$.
A. ${{x}^{2}}{{\text{e}}^{x}}-2\int{x{{\text{e}}^{x}}\text{d}x}$.
B. ${{x}^{2}}{{\text{e}}^{x}}+2\int{x{{\text{e}}^{x}}\text{d}x}$.
C. ${{x}^{2}}{{\text{e}}^{x}}-\int{x{{\text{e}}^{x}}\text{d}x}$.
D. ${{x}^{2}}{{\text{e}}^{x}}+\int{x{{\text{e}}^{x}}\text{d}x}$.
Đặt $\left\{ \begin{aligned}
& u={{x}^{2}} \\
& \text{d}v={{\text{e}}^{x}}\text{d}x \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& \text{d}u=2x\text{d}x \\
& v={{\text{e}}^{x}} \\
\end{aligned} \right.$
Khi đó $\int{{{x}^{2}}{{\text{e}}^{x}}\text{d}x}={{x}^{2}}{{\text{e}}^{x}}-2\int{x{{\text{e}}^{x}}\text{d}x}$.
& u={{x}^{2}} \\
& \text{d}v={{\text{e}}^{x}}\text{d}x \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& \text{d}u=2x\text{d}x \\
& v={{\text{e}}^{x}} \\
\end{aligned} \right.$
Khi đó $\int{{{x}^{2}}{{\text{e}}^{x}}\text{d}x}={{x}^{2}}{{\text{e}}^{x}}-2\int{x{{\text{e}}^{x}}\text{d}x}$.
Đáp án A.