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