\[ \int \frac {x^2}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx \]
Optimal antiderivative \[ \frac {2 \ln \left (d +c \sqrt {b \,x^{3}+a}\right )}{3 b c} \]
command
integrate(x**2/(a*c+b*c*x**3+d*(b*x**3+a)**(1/2)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {2 \left (\begin {cases} \frac {\sqrt {a + b x^{3}}}{d} & \text {for}\: c = 0 \\\frac {\log {\left (c \sqrt {a + b x^{3}} + d \right )}}{c} & \text {otherwise} \end {cases}\right )}{3 b} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________