\[ \int \frac {\sin ^3(a+b x)}{(c+d x)^3} \, dx \]
Optimal antiderivative \[ -\frac {3 b^{2} \cos \left (a -\frac {b c}{d}\right ) \sinIntegral \left (\frac {b c}{d}+b x \right )}{8 d^{3}}+\frac {9 b^{2} \cos \left (3 a -\frac {3 b c}{d}\right ) \sinIntegral \left (\frac {3 b c}{d}+3 b x \right )}{8 d^{3}}+\frac {9 b^{2} \cosineIntegral \left (\frac {3 b c}{d}+3 b x \right ) \sin \left (3 a -\frac {3 b c}{d}\right )}{8 d^{3}}-\frac {3 b^{2} \cosineIntegral \left (\frac {b c}{d}+b x \right ) \sin \left (a -\frac {b c}{d}\right )}{8 d^{3}}-\frac {3 b \cos \left (b x +a \right ) \left (\sin ^{2}\left (b x +a \right )\right )}{2 d^{2} \left (d x +c \right )}-\frac {\sin ^{3}\left (b x +a \right )}{2 d \left (d x +c \right )^{2}} \]
command
integrate(sin(b*x+a)^3/(d*x+c)^3,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 \[ \text {Timed out} \]_______________________________________________________