Đáp án:
$D.\ -5$
Giải thích các bước giải:
$\quad I =\displaystyle\int\limits_0^1\dfrac{x^2 + 2x}{(x+1)^3}dx$
$\Leftrightarrow I = \displaystyle\int\limits_0^1\dfrac{x^2 + 2x +1}{(x+1)^3}dx - \displaystyle\int\limits_0^1\dfrac{1}{(x+1)^3}dx$
$\Leftrightarrow I = \displaystyle\int\limits_0^1\dfrac{1}{x+1}dx - \displaystyle\int\limits_0^1\dfrac{1}{(x+1)^3}dx$
$\Leftrightarrow I = \ln(x+1)\Bigg|_0^1 + \dfrac{1}{2(x+1)^2}\Bigg|_0^1$
$\Leftrightarrow I = \ln2 -\dfrac38$
$\Rightarrow \begin{cases}a =- \dfrac38\\b = 1\end{cases}$
$\Rightarrow 16a + b = -5$
