<s>[INST] Evaluating $\int{{x^2 -1}\over{x^3 \sqrt{2x^4-2x^2+1}}} \mathrm dx$ How to evaluate:
$$\int{{x^2 -1}\over{x^3 \sqrt{2x^4-2x^2+1}}} \mathrm dx$$
 [/INST] HINT:
First put $x^2=y$ in
$$\int{{x^2 -1}\over{x^3 \sqrt{2x^4-2x^2+1}}} \mathrm dx=\int{{x^2 -1}\over{2x^4 \sqrt{2x^4-2x^2+1}}} \mathrm 2xdx$$
to get $$\int \frac{y-1}{2y^2\sqrt{2y^2-2y+1}}dy$$
Now  $2y^2-2y+1=\frac{4y^2-4y+2}2=\frac{(2y-1)^2+1}2$
Put $2y-1=\tan\theta$
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