Đáp án:
$I = 5\ln2 - 2\ln3$
Giải thích các bước giải:
$\quad I =\displaystyle\int\limits_0^1\dfrac{x+4}{x^2 + 3x +2}dx$
$\to I = \displaystyle\int\limits_0^1\left(\dfrac{3}{x+1} - \dfrac{2}{x+2}\right)dx$
$\to I = 3\displaystyle\int\limits_0^1\dfrac{dx}{x+1} - 2\displaystyle\int\limits_0^1\dfrac{dx}{x+2}$
$\to I = 3\ln|x+1|\Bigg|_0^1 - 2\ln|x+2|\Bigg|_0^1$
$\to I = 5\ln2 - 2\ln3$