16.121 Problem number 910

\[ \int \frac {x^{14}}{\left (1-x^4\right )^{3/2}} \, dx \]

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

\[ {\rm integral}\left (\frac {\sqrt {-x^{4} + 1} x^{14}}{x^{8} - 2 \, x^{4} + 1}, x\right ) \]