Chọn phương án A.

$\begin{aligned}
\displaystyle\int\limits_{0}^{\tfrac{1}{2}}\dfrac{2x-1}{x+1}\mathrm{\,d}x&=\int\limits_{0}^{\tfrac{1}{2}}\dfrac{2(x+1)-3}{x+1}\mathrm{\,d}x\\
&=\int\limits_{0}^{\tfrac{1}{2}}\left(2-\dfrac{3}{x+1}\right)\mathrm{\,d}x\\
&=\big(2x-3\ln|x+1|\big)\bigg|_{0}^{\tfrac{1}{2}}\\
&=1-3\ln\dfrac{3}{2}=1-3\ln3+3\ln2.
\end{aligned}$