\[ \int \frac {x^4}{\sqrt {a-b x^4}} \, dx \]
Optimal antiderivative \[ -\frac {x \sqrt {-b \,x^{4}+a}}{3 b}+\frac {a^{\frac {5}{4}} \EllipticF \left (\frac {b^{\frac {1}{4}} x}{a^{\frac {1}{4}}}, i\right ) \sqrt {1-\frac {b \,x^{4}}{a}}}{3 b^{\frac {5}{4}} \sqrt {-b \,x^{4}+a}} \]
command
integrate(x^4/(-b*x^4+a)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\sqrt {-b} \left (\frac {a}{b}\right )^{\frac {3}{4}} {\rm ellipticF}\left (\frac {\left (\frac {a}{b}\right )^{\frac {1}{4}}}{x}, -1\right ) - \sqrt {-b x^{4} + a} x}{3 \, b} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {-b x^{4} + a} x^{4}}{b x^{4} - a}, x\right ) \]