Cho \(I = \int\limits_0^1 {\left( {2x + 1} \right)...

B

- Hướng dẫn giải

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

Khi đó

\(I = \int\limits_0^1 {\left( {2x + 1} \right){e^x}\,dx}  \)

\(= \left( {\left( {2x + 1} \right){e^x}} \right)\left| \begin{array}{l}^1\\_0\end{array} \right. - 2\int\limits_0^1 {{e^x}} dx \)

\(= 3e - 1 - 2\int\limits_0^1 {{e^x}} dx\)