\[ \int \frac {x^{14}}{\left (1-x^4\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {77 \EllipticE \left (x , i\right )}{30}+\frac {77 \EllipticF \left (x , i\right )}{30}+\frac {x^{11}}{2 \sqrt {-x^{4}+1}}+\frac {77 x^{3} \sqrt {-x^{4}+1}}{90}+\frac {11 x^{7} \sqrt {-x^{4}+1}}{18} \]
command
integrate(x^14/(-x^4+1)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {{\left (10 \, x^{12} + 22 \, x^{8} + 154 \, x^{4} - 231\right )} \sqrt {-x^{4} + 1}}{90 \, {\left (x^{5} - x\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {-x^{4} + 1} x^{14}}{x^{8} - 2 \, x^{4} + 1}, x\right ) \]