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