Integrate $\int \frac{x^2-1}{x^3 \sqrt{2x^4-2x^2+1}} \mathop{dx}$ Evaluate $$\int \frac{x^2-1}{x^3 \sqrt{2x^4-2x^2+1}} \mathop{dx}$$
I tried $u=\sqrt{2x^4-2x^2+1}$, $u=\dfrac{1}{x}$ and $u=\sqrt{x}$ but none of these worked.
A friend gave this and said it's from IIT JEE and answer is $$\dfrac{\sqrt{2x^4-2x^2+1}}{2x^2}+C$$
I would like a hint or suggestion.

Substitute $t=\frac1{x^2}$ to get
$$\int \frac{x^2-1}{x^3 \sqrt{2x^4-2x^2+1}} {dx}
 =\frac12 \int \frac{(t-1)dt}{\sqrt{2-2t+t^2}}
=\frac12 \sqrt{2-2t+t^2}+C
$$
