Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\int\limits_{\frac{1}{2}}^1 {f\left( x \right)dx} = 2 - 3\ln 2\\
\Leftrightarrow \int\limits_{\frac{1}{2}}^1 {\left( {\frac{a}{{{x^2}}} + \frac{b}{x} + 2} \right)dx} = 2 - 3\ln 2\\
\Leftrightarrow \mathop {\left. {\left( {\frac{{ - a}}{x} + b.\ln \left| x \right| + 2x} \right)} \right|}\nolimits_{\frac{1}{2}}^1 = 2 - 3\ln 2\\
\Leftrightarrow \left( {\frac{{ - a}}{1} + b.\ln 1 + 2} \right) - \left( {\frac{{ - a}}{{\frac{1}{2}}} + b\ln \frac{1}{2} + 1} \right) = 2 - 3\ln 2\\
\Leftrightarrow a - b\ln \frac{1}{2} + 1 = 2 - 3\ln 2\\
\Leftrightarrow a + b\ln 2 = 1 - 3\ln 2\\
\Rightarrow \left\{ \begin{array}{l}
a = 1\\
b = - 3
\end{array} \right.\\
\Rightarrow T = a + b = - 2
\end{array}\)
