\[ \int \sqrt {1-d x} \sqrt {1+d x} \left (A+B x+C x^2\right ) \, dx \]
Optimal antiderivative \[ -\frac {B \left (-d^{2} x^{2}+1\right )^{\frac {3}{2}}}{3 d^{2}}-\frac {C x \left (-d^{2} x^{2}+1\right )^{\frac {3}{2}}}{4 d^{2}}+\frac {\left (4 A \,d^{2}+C \right ) \arcsin \left (d x \right )}{8 d^{3}}+\frac {\left (4 A \,d^{2}+C \right ) x \sqrt {-d^{2} x^{2}+1}}{8 d^{2}} \]
command
integrate((C*x**2+B*x+A)*(-d*x+1)**(1/2)*(d*x+1)**(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 \[ \text {Timed out} \]_____________________________________________________