Đáp án:
87.C
Giải thích các bước giải:
$\begin{array}{l}
87.\\
\int {\frac{{dx}}{{\sqrt {x + 2} + \sqrt {x + 1} }}} = \int {\left( {\sqrt {x + 2} - \sqrt {x + 1} } \right)dx} \\
= \int {{{\left( {x + 2} \right)}^{\frac{1}{2}}}dx} - \int {{{\left( {x + 1} \right)}^{\frac{1}{2}}}dx} \\
= \frac{{{{\left( {x + 2} \right)}^{\frac{3}{2}}}}}{{\frac{3}{2}}} - \frac{{{{\left( {x + 1} \right)}^{\frac{3}{2}}}}}{{\frac{3}{2}}} + C\\
= \frac{2}{3}\left( {x + 2} \right)\sqrt {x + 2} - \frac{2}{3}\left( {x + 1} \right)\sqrt {x + 1} + C\\
\Rightarrow a = \frac{2}{3},b = - \frac{2}{3} \Rightarrow 3a + b = \frac{4}{3}
\end{array}$
