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I am working on this integral

\[\int \frac{x^{2}+1}{x^{4}+1}dx\]

Now, I have tried this way:

\[u=x^{2}+1\]

after I did:

\[\int \frac{x^{2}+1}{\left ( x^{2}+1 \right )\left ( x^{2}-1 \right )}dx\]

But I got stuck, I got:

\[\frac{1}{2}\cdot \int \frac{1}{u\sqrt{u-1}}dx\]

I thought of making another substitution, but I tried and failed. Help required