indefinite integration $ \int \frac { x^2 dx} {x^4 + x^2 -2}$ problem : $ \int \frac { x^2 dx}  {x^4 + x^2 -2}$
solution : divide numerator and denominator by $x^2$
$ \int \frac { dx}  {x^2 + 1 -\frac{1}{x^2}}$
Now whats the next step $?$
Am I doing right $?$

HINT:
Setting $x^2=y,$
$$A=\frac{x^2}{x^4+x^2-2}=\dfrac y{y^2+y-2}=\dfrac y{(y+2)(y-1)}$$
As $y+2+2(y-1)=3y$
$$3A=\dfrac{y+2+2(y-1)}{(y+2)(y-1)}=\dfrac1{y-1}+\dfrac2{y+2}$$
Replace $y$ with $x^2$
