\[ \int \frac {\cos ^2(a+b x) \sin ^3(a+b x)}{(c+d x)^4} \, dx \]
Optimal antiderivative \[ \frac {125 b^{3} \cosineIntegral \left (\frac {5 b c}{d}+5 b x \right ) \cos \left (5 a -\frac {5 b c}{d}\right )}{96 d^{4}}-\frac {9 b^{3} \cosineIntegral \left (\frac {3 b c}{d}+3 b x \right ) \cos \left (3 a -\frac {3 b c}{d}\right )}{32 d^{4}}-\frac {b^{3} \cosineIntegral \left (\frac {b c}{d}+b x \right ) \cos \left (a -\frac {b c}{d}\right )}{48 d^{4}}-\frac {b \cos \left (b x +a \right )}{48 d^{2} \left (d x +c \right )^{2}}-\frac {b \cos \left (3 b x +3 a \right )}{32 d^{2} \left (d x +c \right )^{2}}+\frac {5 b \cos \left (5 b x +5 a \right )}{96 d^{2} \left (d x +c \right )^{2}}-\frac {125 b^{3} \sinIntegral \left (\frac {5 b c}{d}+5 b x \right ) \sin \left (5 a -\frac {5 b c}{d}\right )}{96 d^{4}}+\frac {9 b^{3} \sinIntegral \left (\frac {3 b c}{d}+3 b x \right ) \sin \left (3 a -\frac {3 b c}{d}\right )}{32 d^{4}}+\frac {b^{3} \sinIntegral \left (\frac {b c}{d}+b x \right ) \sin \left (a -\frac {b c}{d}\right )}{48 d^{4}}-\frac {\sin \left (b x +a \right )}{24 d \left (d x +c \right )^{3}}+\frac {b^{2} \sin \left (b x +a \right )}{48 d^{3} \left (d x +c \right )}-\frac {\sin \left (3 b x +3 a \right )}{48 d \left (d x +c \right )^{3}}+\frac {3 b^{2} \sin \left (3 b x +3 a \right )}{32 d^{3} \left (d x +c \right )}+\frac {\sin \left (5 b x +5 a \right )}{48 d \left (d x +c \right )^{3}}-\frac {25 b^{2} \sin \left (5 b x +5 a \right )}{96 d^{3} \left (d x +c \right )} \]
command
integrate(cos(b*x+a)^2*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 \[ \text {Timed out} \]_______________________________________________________