Giải thích các bước giải:
$\begin{array}{l}
\int\limits_2^3 {\dfrac{{2x}}{{\left( {{x^2} - 1} \right)\left( {x + 1} \right)}}dx} \\
= \int\limits_2^3 {\dfrac{{x + 1 + x - 1}}{{{{\left( {x - 1} \right)}^2}\left( {x + 1} \right)}}dx} \\
= \int\limits_2^3 {\left( {\dfrac{1}{{{{\left( {x - 1} \right)}^2}}} + \dfrac{1}{{\left( {x - 1} \right)\left( {x + 1} \right)}}} \right)dx} \\
= \int\limits_2^3 {\left( {\dfrac{1}{{{{\left( {x - 1} \right)}^2}}} + \dfrac{1}{2}\left( {\dfrac{1}{{x - 1}} - \dfrac{1}{{x + 1}}} \right)} \right)dx} \\
= \left( {\dfrac{{ - 1}}{{x - 1}} + \dfrac{1}{2}\ln \left| {\dfrac{{x - 1}}{{x + 1}}} \right|} \right)|_2^3\\
= \dfrac{1}{2} - \dfrac{1}{2}\ln 2 + \dfrac{1}{2}\ln 3
\end{array}$
