\[ \int (e+f x)^2 \sin \left (a+\frac {b}{\sqrt [3]{c+d x}}\right ) \, dx \]
Optimal antiderivative \[ -\frac {b^{9} f^{2} \cosineIntegral \left (\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right ) \cos \left (a \right )}{120960 d^{3}}+\frac {b^{3} \left (-c f +d e \right )^{2} \cosineIntegral \left (\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right ) \cos \left (a \right )}{2 d^{3}}+\frac {b^{5} f \left (-c f +d e \right ) \left (d x +c \right )^{\frac {1}{3}} \cos \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{120 d^{3}}-\frac {b^{7} f^{2} \left (d x +c \right )^{\frac {2}{3}} \cos \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{120960 d^{3}}+\frac {b \left (-c f +d e \right )^{2} \left (d x +c \right )^{\frac {2}{3}} \cos \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{2 d^{3}}-\frac {b^{3} f \left (-c f +d e \right ) \left (d x +c \right ) \cos \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{60 d^{3}}+\frac {b^{5} f^{2} \left (d x +c \right )^{\frac {4}{3}} \cos \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{20160 d^{3}}+\frac {b f \left (-c f +d e \right ) \left (d x +c \right )^{\frac {5}{3}} \cos \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{5 d^{3}}-\frac {b^{3} f^{2} \left (d x +c \right )^{2} \cos \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{1008 d^{3}}+\frac {b \,f^{2} \left (d x +c \right )^{\frac {8}{3}} \cos \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{24 d^{3}}+\frac {b^{6} f \left (-c f +d e \right ) \cos \left (a \right ) \sinIntegral \left (\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{120 d^{3}}+\frac {b^{6} f \left (-c f +d e \right ) \cosineIntegral \left (\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right ) \sin \left (a \right )}{120 d^{3}}+\frac {b^{9} f^{2} \sinIntegral \left (\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right ) \sin \left (a \right )}{120960 d^{3}}-\frac {b^{3} \left (-c f +d e \right )^{2} \sinIntegral \left (\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right ) \sin \left (a \right )}{2 d^{3}}+\frac {b^{8} f^{2} \left (d x +c \right )^{\frac {1}{3}} \sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{120960 d^{3}}-\frac {b^{2} \left (-c f +d e \right )^{2} \left (d x +c \right )^{\frac {1}{3}} \sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{2 d^{3}}+\frac {b^{4} f \left (-c f +d e \right ) \left (d x +c \right )^{\frac {2}{3}} \sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{120 d^{3}}-\frac {b^{6} f^{2} \left (d x +c \right ) \sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{60480 d^{3}}+\frac {\left (-c f +d e \right )^{2} \left (d x +c \right ) \sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{d^{3}}-\frac {b^{2} f \left (-c f +d e \right ) \left (d x +c \right )^{\frac {4}{3}} \sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{20 d^{3}}+\frac {b^{4} f^{2} \left (d x +c \right )^{\frac {5}{3}} \sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{5040 d^{3}}+\frac {f \left (-c f +d e \right ) \left (d x +c \right )^{2} \sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{d^{3}}-\frac {b^{2} f^{2} \left (d x +c \right )^{\frac {7}{3}} \sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{168 d^{3}}+\frac {f^{2} \left (d x +c \right )^{3} \sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {1}{3}}}\right )}{3 d^{3}} \]
command
integrate((f*x+e)^2*sin(a+b/(d*x+c)^(1/3)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________