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