\[ \int \frac {x^6 \left (A+B x+C x^2\right )}{\left (a+b x^2\right )^{9/2}} \, dx \]
Optimal antiderivative \[ -\frac {x^{6} \left (B a -\left (A b -a C \right ) x \right )}{7 a b \left (b \,x^{2}+a \right )^{\frac {7}{2}}}-\frac {x^{4} \left (7 C x +6 B \right )}{35 b^{2} \left (b \,x^{2}+a \right )^{\frac {5}{2}}}-\frac {x^{2} \left (35 C x +24 B \right )}{105 b^{3} \left (b \,x^{2}+a \right )^{\frac {3}{2}}}+\frac {C \arctanh \left (\frac {x \sqrt {b}}{\sqrt {b \,x^{2}+a}}\right )}{b^{\frac {9}{2}}}+\frac {-35 C x -16 B}{35 b^{4} \sqrt {b \,x^{2}+a}} \]
command
integrate(x**6*(C*x**2+B*x+A)/(b*x**2+a)**(9/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________