I wish to integrate
$$\int \frac{1+x^2}{(1-x^2)\sqrt{1+x^4}}\ dx.$$
I have tried substituting $x = \sqrt{\mathrm{tan}\ u}$ but then I get a root at the bottom which I can't get rid of. Also I have tried $x = \tan u$ but that isn't any better.
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try $t=\frac{1}{x}$. – hamam_Abdallah Oct 15 '16 at 00:04
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@AbdallahHammam I tried that but I get the exact same integral again – Nanoputian Oct 16 '16 at 20:44
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Mathematica: $$\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}$$ – David G. Stork Apr 29 '25 at 15:41