\[ \int x \left (a+b x^2\right )^2 \left (A+B x+C x^2+D x^3\right ) \, dx \]
Optimal antiderivative \[ \frac {a^{2} B \,x^{3}}{3}+\frac {a^{2} C \,x^{4}}{4}+\frac {a \left (2 b B +a D\right ) x^{5}}{5}+\frac {a b C \,x^{6}}{3}+\frac {b \left (b B +2 a D\right ) x^{7}}{7}+\frac {b^{2} C \,x^{8}}{8}+\frac {b^{2} D x^{9}}{9}+\frac {A \left (b \,x^{2}+a \right )^{3}}{6 b} \]
command
integrate(x*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {1}{9} \, D b^{2} x^{9} + \frac {1}{8} \, C b^{2} x^{8} + \frac {1}{7} \, {\left (2 \, D a b + B b^{2}\right )} x^{7} + \frac {1}{6} \, {\left (2 \, C a b + A b^{2}\right )} x^{6} + \frac {1}{3} \, B a^{2} x^{3} + \frac {1}{5} \, {\left (D a^{2} + 2 \, B a b\right )} x^{5} + \frac {1}{2} \, A a^{2} x^{2} + \frac {1}{4} \, {\left (C a^{2} + 2 \, A a b\right )} x^{4} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]