Question with Solution

$$\begin{array}{rlr}& \int \frac{\left(x^8+4+4x^4\right)-4x^4}{x^4-2x^2+2}dx=\int \frac{{\left(x^4+2\right)}^2-{\left(2x^2\right)}^2}{\left(x^4-2x^2+2\right)}dx& =\int \frac{\left(x^4+2-2x^2\right)\left(x^4+2+2x^2\right)}{\left(x^4-2x^2+2\right)}dx=\frac{x^5}{5}+\frac{2x^3}{3}+2x+C\end{array}$$