The puzzle was to compute
$$ \int \frac{1+x^2}{(1-x^2)\sqrt{1+x^4}} dx$$
Solution
As usual, a clever substitution needs to be sought.
In this case, you divide the numerator and denominator by $x^2$ and then make the substitution $t = x - \frac{1}{x}$.
This results in
$$ -\int \frac{dt}{t\sqrt{t^2+1}}$$
which is a standard integral.
$$ \int \frac{1+x^2}{(1-x^2)\sqrt{1+x^4}} dx$$
Solution
As usual, a clever substitution needs to be sought.
In this case, you divide the numerator and denominator by $x^2$ and then make the substitution $t = x - \frac{1}{x}$.
This results in
$$ -\int \frac{dt}{t\sqrt{t^2+1}}$$
which is a standard integral.
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