​ Tìm ∫xexdx ​

Question

Tìm \(\int xe^{x} {\rm d}x \)
 

A. \(e^{x} \left(x-1\right)+C. \)

B. \( e^{x} \left(x+1\right)+C. \)

C. \(e^{x} \left(x+1\right)+x+C. \)

D. \(e^{x} \left(x+1\right)+2x+C. \)

Answer 1

Chọn A

Đặt \(\left\{\begin{array}{l} {u=x} \\ {{\rm d}v=e^{x} {\rm d}x} \end{array}\right. \Rightarrow \left\{\begin{array}{l} {{\rm d}u={\rm d}x} \\ {v=e^{x} } \end{array}\right. \)

\(\Rightarrow \int xe^{x} {\rm d}x =xe^{x} -\int e^{x} {\rm d}x \)

\(=\, xe^{x} -e^{x} +C=e^{x} \left(x-1\right)+C\)