\[ \int \frac {x^3 \sin (c+d x)}{(a+b x)^3} \, dx \]
Optimal antiderivative \[ \frac {3 a^{2} d \cosineIntegral \left (\frac {a d}{b}+d x \right ) \cos \left (-c +\frac {a d}{b}\right )}{b^{5}}-\frac {\cos \left (d x +c \right )}{b^{3} d}+\frac {a^{3} d \cos \left (d x +c \right )}{2 b^{5} \left (b x +a \right )}-\frac {3 a \cos \left (-c +\frac {a d}{b}\right ) \sinIntegral \left (\frac {a d}{b}+d x \right )}{b^{4}}+\frac {a^{3} d^{2} \cos \left (-c +\frac {a d}{b}\right ) \sinIntegral \left (\frac {a d}{b}+d x \right )}{2 b^{6}}+\frac {3 a \cosineIntegral \left (\frac {a d}{b}+d x \right ) \sin \left (-c +\frac {a d}{b}\right )}{b^{4}}-\frac {a^{3} d^{2} \cosineIntegral \left (\frac {a d}{b}+d x \right ) \sin \left (-c +\frac {a d}{b}\right )}{2 b^{6}}+\frac {3 a^{2} d \sinIntegral \left (\frac {a d}{b}+d x \right ) \sin \left (-c +\frac {a d}{b}\right )}{b^{5}}+\frac {a^{3} \sin \left (d x +c \right )}{2 b^{4} \left (b x +a \right )^{2}}-\frac {3 a^{2} \sin \left (d x +c \right )}{b^{4} \left (b x +a \right )} \]
command
integrate(x^3*sin(d*x+c)/(b*x+a)^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 \[ \text {Timed out} \]_______________________________________________________