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