Biết \(\int\limits_3^5 {\fr...

D

- Hướng dẫn giải

\(\int\limits_3^5 {\frac{{{x^2} + x + 1}}{{x + 1}}} dx = \int\limits_3^5 {\left( {x + \frac{1}{{x + 1}}} \right)dx = \left( {\frac{{{x^2}}}{2} + \ln \left| {x + 1} \right|} \right)\left| \begin{array}{l}^5\\_3\end{array} \right. = 8 + \ln \frac{3}{2} \Rightarrow \left\{ \begin{array}{l}a = 8\\b = 3\end{array} \right. \Rightarrow S = a - 2b = 2.} \)