\[ \int x^2 \left (a+b x^2+c x^4\right )^p \left (3 a+b (5+2 p) x^2+c (7+4 p) x^4\right ) \, dx \]
Optimal antiderivative \[ x^{3} \left (c \,x^{4}+b \,x^{2}+a \right )^{1+p} \]
command
integrate(x**2*(c*x**4+b*x**2+a)**p*(3*a+b*(5+2*p)*x**2+c*(7+4*p)*x**4),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ a x^{3} \left (a + b x^{2} + c x^{4}\right )^{p} + b x^{5} \left (a + b x^{2} + c x^{4}\right )^{p} + c x^{7} \left (a + b x^{2} + c x^{4}\right )^{p} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________