Giải thích các bước giải:
Ta có : $f'(x)=-\dfrac{2a}{x^3}-\dfrac{b}{x^2}$
$\to -\dfrac{2a}{(\dfrac{1}{2})^3}-\dfrac{b}{(\dfrac{1}{2})^2}=4$
$\to 4a+b=-1\to b=-(4a+1)$
Lại có :
$\int^1_{\frac{1}{2}}\dfrac{a}{x^2}+\dfrac{b}{x}+2dx=2-3\ln 2$
$\to -\dfrac{a}{x}+b\ln \left|x\right|+2x|^1_{\frac{1}{2}}=2-3\ln2$
$\to a+b\ln 2+\dfrac{3}{8}=2-3\ln2$
$\to a+b\ln 2=\dfrac{13}{8}-3\ln2$
$\to a+(-(4a+1))\ln 2=\dfrac{13}{8}-3\ln2$
$\to a=\dfrac{13-16\ln \left(2\right)}{8\left(1-4\ln \left(2\right)\right)}$
$\to b=-\dfrac{96\ln \left(2\right)-60}{8\left(-4\ln \left(2\right)+1\right)}$
