Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\int {\frac{{2{x^2} + 2x + 3}}{{2x + 1}}dx} \\
= \frac{1}{2}\int {\frac{{4{x^2} + 4x + 6}}{{2x + 1}}dx} \\
= \frac{1}{2}\int {\frac{{{{\left( {2x + 1} \right)}^2} + 5}}{{2x + 1}}dx} \\
= \frac{1}{2}\int {\left[ {\left( {2x + 1} \right) + \frac{5}{{2x + 1}}} \right]dx} \\
= \frac{1}{2}\left[ {\int {\left( {2x + 1} \right)dx} + \int {\frac{5}{{2x + 1}}dx} } \right]\\
= \frac{1}{2}.\left[ {{x^2} + x + \frac{1}{2}\int {\frac{{5d\left( {2x + 1} \right)}}{{2x + 1}}} } \right]\\
= \frac{1}{2}\left( {{x^2} + x + \frac{5}{2}.ln\left| {2x + 1} \right|} \right)
\end{array}\)
