解答

$${I=\int\left(x-\frac{1}{x^2}\right)^2dx}$$

$$\begin{eqnarray*} I&=& \int(x-x^{-2})^2dx\\ &=&\int(x^2-2x\times x^{-2}+x^{-4... ...ac{1}{3}x^{-3}+C\\ &=& \frac{1}{3}x^3-\frac{1}{3x^3}-2\log x+C \end{eqnarray*}$$