\[ \int \frac {\cos ^3(a+b x) \sin ^2(a+b x)}{(c+d x)^3} \, dx \]
Optimal antiderivative \[ \frac {25 b^{2} \cosineIntegral \left (\frac {5 b c}{d}+5 b x \right ) \cos \left (5 a -\frac {5 b c}{d}\right )}{32 d^{3}}+\frac {9 b^{2} \cosineIntegral \left (\frac {3 b c}{d}+3 b x \right ) \cos \left (3 a -\frac {3 b c}{d}\right )}{32 d^{3}}-\frac {b^{2} \cosineIntegral \left (\frac {b c}{d}+b x \right ) \cos \left (a -\frac {b c}{d}\right )}{16 d^{3}}-\frac {\cos \left (b x +a \right )}{16 d \left (d x +c \right )^{2}}+\frac {\cos \left (3 b x +3 a \right )}{32 d \left (d x +c \right )^{2}}+\frac {\cos \left (5 b x +5 a \right )}{32 d \left (d x +c \right )^{2}}-\frac {25 b^{2} \sinIntegral \left (\frac {5 b c}{d}+5 b x \right ) \sin \left (5 a -\frac {5 b c}{d}\right )}{32 d^{3}}-\frac {9 b^{2} \sinIntegral \left (\frac {3 b c}{d}+3 b x \right ) \sin \left (3 a -\frac {3 b c}{d}\right )}{32 d^{3}}+\frac {b^{2} \sinIntegral \left (\frac {b c}{d}+b x \right ) \sin \left (a -\frac {b c}{d}\right )}{16 d^{3}}+\frac {b \sin \left (b x +a \right )}{16 d^{2} \left (d x +c \right )}-\frac {3 b \sin \left (3 b x +3 a \right )}{32 d^{2} \left (d x +c \right )}-\frac {5 b \sin \left (5 b x +5 a \right )}{32 d^{2} \left (d x +c \right )} \]
command
integrate(cos(b*x+a)^3*sin(b*x+a)^2/(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 \[ \text {Timed out} \]_______________________________________________________