\[ \int \frac {\left (-1+x^2\right ) \left (1+x^2\right )^3 \sqrt {1+2 x^2+x^4}}{\left (1+x^4\right ) \left (1-x^2+x^4-x^6+x^8\right )} \, dx \]
Optimal antiderivative \[ \mathit {Unintegrable} \]
command
integrate((x**2-1)*(x**2+1)**3*((x**2+1)**2)**(1/2)/(x**4+1)/(x**8-x**6+x**4-x**2+1),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \sqrt {2} \log {\left (- \sqrt {2} x + \sqrt {\left (x^{2} + 1\right )^{2}} \right )} + \sqrt {2} \log {\left (\sqrt {2} x + \sqrt {\left (x^{2} + 1\right )^{2}} \right )} + \operatorname {RootSum} {\left (16 t^{4} - 20 t^{2} + 5, \left ( t \mapsto t \log {\left (x \left (\frac {48 t^{5}}{29} - \frac {60 t^{3}}{29} - \frac {43 t}{29}\right ) + \sqrt {\left (x^{2} + 1\right )^{2}} \right )} \right )\right )} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Exception raised: SympifyError} \]________________________________________________________________________________________