\[ \int \frac {\cos (a+b x) \sin ^3(a+b x)}{(c+d x)^3} \, dx \]
Optimal antiderivative \[ -\frac {b \cos \left (2 b x +2 a \right )}{4 d^{2} \left (d x +c \right )}+\frac {b \cos \left (4 b x +4 a \right )}{4 d^{2} \left (d x +c \right )}-\frac {b^{2} \cos \left (2 a -\frac {2 b c}{d}\right ) \sinIntegral \left (\frac {2 b c}{d}+2 b x \right )}{2 d^{3}}+\frac {b^{2} \cos \left (4 a -\frac {4 b c}{d}\right ) \sinIntegral \left (\frac {4 b c}{d}+4 b x \right )}{d^{3}}+\frac {b^{2} \cosineIntegral \left (\frac {4 b c}{d}+4 b x \right ) \sin \left (4 a -\frac {4 b c}{d}\right )}{d^{3}}-\frac {b^{2} \cosineIntegral \left (\frac {2 b c}{d}+2 b x \right ) \sin \left (2 a -\frac {2 b c}{d}\right )}{2 d^{3}}-\frac {\sin \left (2 b x +2 a \right )}{8 d \left (d x +c \right )^{2}}+\frac {\sin \left (4 b x +4 a \right )}{16 d \left (d x +c \right )^{2}} \]
command
integrate(cos(b*x+a)*sin(b*x+a)^3/(d*x+c)^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 \[ \text {Timed out} \]_______________________________________________________