Tính tích phân $\displaystyle\int\limits_{1}^{2}\left(x^2+4x+\dfrac{4}{x^2}\right)\mathrm{\,d}x$.
$\displaystyle\int\limits_{1}^{2}\left(x^2+4x+\dfrac{4}{x^2}\right)\mathrm{\,d}x=\left(\dfrac{x^3}{3}+2x^2-\dfrac{4}{x}\right)\bigg|_1^2=\dfrac{31}{3}$.