Đáp án:
$I = -\dfrac23\ln2$
Giải thích các bước giải:
$\quad I =\displaystyle\int\limits_0^1\dfrac{dx}{x^2 - x -2}$
$\to I = \displaystyle\int\limits_0^1\left(\dfrac{1}{3(x-2)} -\dfrac{1}{3(x+1)}\right)dx$
$\to I =\dfrac13\displaystyle\int\limits_0^1\dfrac{dx}{x-2} - \dfrac13\displaystyle\int\limits_0^1\dfrac{dx}{x+1}$
$\to I =\dfrac13\ln|x-2|\Bigg|_0^1 - \dfrac13\ln|x+1|\Bigg|_0^1$
$\to I = -\dfrac23\ln2$
