Tìm nguyên hàm \(I = \int {\left( {2x - 1} \right){e^{ - x}}dx} .\)

Tìm nguyên hàm \(I = \int {\left( {2x - 1} \right){e^{ - x}}dx} .\)
A. \(I = - \left( {2x + 1} \right){e^{ - x}} + C\)
B. \(I = - \left( {2x - 1} \right){e^{ - x}} + C\)
C. \(I = - \left( {2x + 3} \right){e^{ - x}} + C\)
D. \(I = - \left( {2x - 3} \right){e^{ - x}} + C\)

Đặt: \(\left\{ \begin{array}{l} u = 2x - 1\\ dv = {e^{ - x}}dx \end{array} \right. \Rightarrow \left\{ \begin{array}{l} du = 2dx\\ v = - {e^{ - x}} \end{array} \right.\)
\(\begin{array}{l} \int {\left( {2x - 1} \right){e^{ - x}}dx} = - \left( {2x - 1} \right){e^{ - x}} + 2\int {{e^{ - x}}dx} \\ = - \left( {2x - 1} \right){e^{ - x}} - 2{e^{ - x}} + C = \left( { - 2x - 1} \right){e^{ - x}} + C \end{array}\)