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