\[ \int \frac {\cos ^3(a+b x) \sin ^3(a+b x)}{(c+d x)^4} \, dx \]
Optimal antiderivative \[ \frac {9 b^{3} \cosineIntegral \left (\frac {6 b c}{d}+6 b x \right ) \cos \left (6 a -\frac {6 b c}{d}\right )}{8 d^{4}}-\frac {b^{3} \cosineIntegral \left (\frac {2 b c}{d}+2 b x \right ) \cos \left (2 a -\frac {2 b c}{d}\right )}{8 d^{4}}-\frac {b \cos \left (2 b x +2 a \right )}{32 d^{2} \left (d x +c \right )^{2}}+\frac {b \cos \left (6 b x +6 a \right )}{32 d^{2} \left (d x +c \right )^{2}}-\frac {9 b^{3} \sinIntegral \left (\frac {6 b c}{d}+6 b x \right ) \sin \left (6 a -\frac {6 b c}{d}\right )}{8 d^{4}}+\frac {b^{3} \sinIntegral \left (\frac {2 b c}{d}+2 b x \right ) \sin \left (2 a -\frac {2 b c}{d}\right )}{8 d^{4}}-\frac {\sin \left (2 b x +2 a \right )}{32 d \left (d x +c \right )^{3}}+\frac {b^{2} \sin \left (2 b x +2 a \right )}{16 d^{3} \left (d x +c \right )}+\frac {\sin \left (6 b x +6 a \right )}{96 d \left (d x +c \right )^{3}}-\frac {3 b^{2} \sin \left (6 b x +6 a \right )}{16 d^{3} \left (d x +c \right )} \]
command
integrate(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c)^4,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 \[ \text {Timed out} \]_______________________________________________________