\[ \int \frac {-1+x^{10}}{\sqrt {1+x^4} \left (1+x^{10}\right )} \, dx \]
Optimal antiderivative \[ -\frac {\arctan \left (\frac {\sqrt {2}\, x}{\sqrt {x^{4}+1}}\right ) \sqrt {2}}{10}-\frac {\sqrt {2+2 \sqrt {5}}\, \arctan \left (\frac {\sqrt {-2+2 \sqrt {5}}\, x}{2 \sqrt {x^{4}+1}}\right )}{5}-\frac {\sqrt {-2+2 \sqrt {5}}\, \operatorname {arctanh}\left (\frac {\sqrt {2+2 \sqrt {5}}\, x}{2 \sqrt {x^{4}+1}}\right )}{5} \]
command
Int[(-1 + x^10)/(Sqrt[1 + x^4]*(1 + x^10)),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \text {output too large to display} \]
Rubi 4.16.1 under Mathematica 13.3.1 output \[ \int \frac {-1+x^{10}}{\sqrt {1+x^4} \left (1+x^{10}\right )} \, dx \]__________________________________________