<s>[INST] 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 $?$
 [/INST] You are better off using partial fractions, which you should know if you have been given this integral to evaluate.  You have the following factors for the denominator:
$x^4+x^2-2
= (x^2-1)(x^2+2)
= (x+1)(x-1)(x^2+2)$
And then
$x^2/(x^4+x^2-2) = a/(x+1)+b/(x-1)+(cx+d)/(x^2+2)$
You are to find the condtants a, b, c, d that fit this equation.  Then you integrate the resulting partial fractions using logatlrithms and inverse tangents, and add those partial integrals up. 
</s>