Giải thích các bước giải:
Bài 1:
$\int^2_1\dfrac{3x^3+x^2-2}{x+4}dx$
$=\int^2_13x^2-11x+44-\dfrac{178}{x+4}dx$
$=x^3-\dfrac{11}{2}x^2+44x-178\ln|x+4|\Big|^2_1$
$=178\ln6+178\ln5+\dfrac{69}{2}$
Bài 2:
$\int^{-1}_{-2}\dfrac{x^2+x+5}{x-1}dx$
$=\int^{-1}_{-2}x+2+\dfrac{7}{x-1}dx$
$=\dfrac{x^2}{2}+2x+7\ln|x-1|\Big|^{-1}_{-2}$
$=7\ln2+\dfrac{1}{2}-7\ln3$
$=\dfrac 12-7\ln\dfrac32$
$\to a^2-b=\dfrac{29}4$
