\[ \int \csc ^6(c+b x) \sin (a+b x) \, dx \]
Optimal antiderivative \[ -\frac {3 \arctanh \left (\cos \left (b x +c \right )\right ) \cos \left (a -c \right )}{8 b}-\frac {3 \cos \left (a -c \right ) \cot \left (b x +c \right ) \csc \left (b x +c \right )}{8 b}-\frac {\cos \left (a -c \right ) \cot \left (b x +c \right ) \left (\csc ^{3}\left (b x +c \right )\right )}{4 b}-\frac {\left (\csc ^{5}\left (b x +c \right )\right ) \sin \left (a -c \right )}{5 b} \]
command
integrate(csc(b*x+c)^6*sin(b*x+a),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 \[ \text {Exception raised: NotImplementedError} \]_______________________________________________________