Ta có: \(\int \frac{x^{2} -1}{x^{4} +1} dx=\int \frac{1-\frac{1}{x^{2} } }{x^{2} +\frac{1}{x^{2} } } {\rm d}x=\int \frac{{\rm d}\left(x+\frac{1}{x} \right)}{\left(x+\frac{1}{x} \right)^{2} -2} \)
\(=\frac{1}{2\sqrt{2} } \ln \frac{x+\frac{1}{x} -\sqrt{2} }{x+\frac{1}{x} +\sqrt{2} } +C. \)