\[ \int \frac {\sqrt {c+d x} \sqrt {e+f x} \left (A+B x+C x^2\right )}{(a+b x)^{9/2}} \, dx \]
Optimal antiderivative \[ \text {Expression too large to display} \]
command
integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(9/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \text {output too large to display} \]
Fricas 1.3.7 via sagemath 9.3 output \[ {\rm integral}\left (\frac {{\left (C x^{2} + B x + A\right )} \sqrt {b x + a} \sqrt {d x + c} \sqrt {f x + e}}{b^{5} x^{5} + 5 \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x^{3} + 10 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b x + a^{5}}, x\right ) \]