Giải thích các bước giải:
$\begin{split}\dfrac{1}{x^3(x^2+1)}&=\dfrac{x^2+1-x^2}{x^3(x^2+1))}\\&=\dfrac{1}{x^3}-\dfrac{1}{x(x^2+1)}\\&=\dfrac{1}{x^3}-\dfrac{x^2+1-x^2}{x(x^2+1)}\\&=\dfrac{1}{x^3}-(\dfrac{1}{x}-\dfrac{x}{x^2+1})\\&=\dfrac{1}{x^3}-\dfrac{1}{x}+\dfrac{x}{x^2+1}\end{split}$