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