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