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* Hướng dẫn giải

Đáp án B

Đặt $\left\{\begin{array}{l}u=2x-1\\ dx=e^{x}dx\end{array}\right.\Rightarrow \left\{\begin{array}{l}du=2dx\\ v=e^x\end{array}\right.$. Khi đó: $\underset{0}{\overset{m}{\int }}\left(2x-1\right)e^{x}dx=\left(2x-1\right){\left.e^x\right|}_0^m-2\underset{0}{\overset{m}{\int }}{e}^{x}dx=\left(2m-1\right)e^m+1-{\left.2e^x\right|}_0^m=\left(2m-3\right)e^m+3$

Suy ra: $\left(2m-3\right)e^m+3=4m-3\iff \left(2m-3\right)e^m=2\left(2m-3\right)$

$\iff \left[\begin{array}{l}2m-3=0\\ e^m=2\end{array}\right.\stackrel{0<m<1}{\to }{e}^m=2\iff m=\ln 2\approx 0,693$ gần giá trị 0,69 nhất