\[ \int \frac {1}{\sqrt [4]{1+x^4}} \, dx \]
Optimal antiderivative \[ \frac {\arctan \! \left (\frac {x}{\left (x^{4}+1\right )^{\frac {1}{4}}}\right )}{2}+\frac {\arctanh \! \left (\frac {x}{\left (x^{4}+1\right )^{\frac {1}{4}}}\right )}{2} \]
command
integrate(1/(x^4+1)^(1/4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ -\frac {1}{2} \, \arctan \left (\frac {{\left (x^{4} + 1\right )}^{\frac {1}{4}}}{x}\right ) + \frac {1}{4} \, \log \left (\frac {{\left (x^{4} + 1\right )}^{\frac {1}{4}}}{x} + 1\right ) - \frac {1}{4} \, \log \left (\frac {{\left (x^{4} + 1\right )}^{\frac {1}{4}}}{x} - 1\right ) \]