\[ \int \frac {\cos ^3(a+b x) \sin ^2(a+b x)}{(c+d x)^2} \, dx \]
Optimal antiderivative \[ -\frac {\cos \left (b x +a \right )}{8 d \left (d x +c \right )}+\frac {\cos \left (3 b x +3 a \right )}{16 d \left (d x +c \right )}+\frac {\cos \left (5 b x +5 a \right )}{16 d \left (d x +c \right )}-\frac {b \cos \left (a -\frac {b c}{d}\right ) \sinIntegral \left (\frac {b c}{d}+b x \right )}{8 d^{2}}+\frac {3 b \cos \left (3 a -\frac {3 b c}{d}\right ) \sinIntegral \left (\frac {3 b c}{d}+3 b x \right )}{16 d^{2}}+\frac {5 b \cos \left (5 a -\frac {5 b c}{d}\right ) \sinIntegral \left (\frac {5 b c}{d}+5 b x \right )}{16 d^{2}}+\frac {5 b \cosineIntegral \left (\frac {5 b c}{d}+5 b x \right ) \sin \left (5 a -\frac {5 b c}{d}\right )}{16 d^{2}}+\frac {3 b \cosineIntegral \left (\frac {3 b c}{d}+3 b x \right ) \sin \left (3 a -\frac {3 b c}{d}\right )}{16 d^{2}}-\frac {b \cosineIntegral \left (\frac {b c}{d}+b x \right ) \sin \left (a -\frac {b c}{d}\right )}{8 d^{2}} \]
command
integrate(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c)^2,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 \[ \text {Timed out} \]_______________________________________________________