Biết rằng $\int\limits_{0}^{1}{\dfrac{x-1}{{{x}^{2}}+3x+2}dx}=a\ln...

Phân tích
$\dfrac{x-1}{{{x}^{2}}+3x+2}=\dfrac{x-1}{\left( x+1 \right)\left( x+2 \right)}=\dfrac{m}{x+1}+\dfrac{n}{x+2}\Rightarrow x-1=m\left( x+2 \right)+n\left( x+1 \right).$
Cho
$\left\{ \begin{aligned}
& x=-1\Rightarrow m=-2 \\
& x=-2\Rightarrow n=3 \\
\end{aligned} \right.\Rightarrow \int\limits_{0}^{1}{\dfrac{x-1}{{{x}^{2}}+3x+2}}dx=\int\limits_{0}^{1}{\left( \dfrac{3}{x+2}-\dfrac{2}{x+1} \right)dx}=3\ln \left| x+2 \right|\left| _{\begin{smallmatrix}
\\
0
\end{smallmatrix}}^{\begin{smallmatrix}
1 \\

\end{smallmatrix}} \right.$
$\Rightarrow I=\left( 3\ln 3-3\ln 2 \right)-2\ln 2=3\ln 3-5\ln 2\Rightarrow a=-5,b=3\Rightarrow S=-98$