\[ \int \frac {\left (c+d x+e x^2\right )^3}{\sqrt {a+b x}} \, dx \]
Optimal antiderivative \[ \frac {2 \left (-2 a e +b d \right ) \left (a^{2} e -a b d +b^{2} c \right )^{2} \left (b x +a \right )^{\frac {3}{2}}}{b^{7}}-\frac {6 \left (a^{2} e -a b d +b^{2} c \right ) \left (5 a b d e -5 a^{2} e^{2}-b^{2} \left (c e +d^{2}\right )\right ) \left (b x +a \right )^{\frac {5}{2}}}{5 b^{7}}-\frac {2 \left (-2 a e +b d \right ) \left (10 a b d e -10 a^{2} e^{2}-b^{2} \left (6 c e +d^{2}\right )\right ) \left (b x +a \right )^{\frac {7}{2}}}{7 b^{7}}-\frac {2 e \left (5 a b d e -5 a^{2} e^{2}-b^{2} \left (c e +d^{2}\right )\right ) \left (b x +a \right )^{\frac {9}{2}}}{3 b^{7}}+\frac {6 e^{2} \left (-2 a e +b d \right ) \left (b x +a \right )^{\frac {11}{2}}}{11 b^{7}}+\frac {2 e^{3} \left (b x +a \right )^{\frac {13}{2}}}{13 b^{7}}+\frac {2 \left (a^{2} e -a b d +b^{2} c \right )^{3} \sqrt {b x +a}}{b^{7}} \]
command
integrate((e*x**2+d*x+c)**3/(b*x+a)**(1/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________