Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
\int\limits_1^{\frac{1}{3}} {\frac{{x - 5}}{{2\left( {x + 1} \right)}}} dx = \int\limits_1^{\frac{1}{3}} {\frac{{x + 1 - 6}}{{2\left( {x + 1} \right)}}dx = \int\limits_1^{\frac{1}{3}} {(\frac{1}{2} - \frac{3}{{x + 1}})} } dx\\
= \frac{1}{2}x\left| {_1^{\frac{1}{3}}} \right. - 3.\ln \left( {x + 1} \right)\left| {_1^{\frac{1}{3}}} \right. = \frac{1}{6} - \frac{1}{2} - 3\ln \frac{4}{3} + 3\ln 2\\
= - \frac{1}{3} - 3\left( {\ln \frac{2}{3}} \right) = \frac{{ - 1}}{3} - \ln \frac{8}{{27}}
\end{array}\)
