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