\[ \int (a+b \sin (c+d x)) \tan ^3(c+d x) \, dx \]
Optimal antiderivative \[ \frac {\left (2 a +3 b \right ) \ln \left (1-\sin \left (d x +c \right )\right )}{4 d}+\frac {\left (2 a -3 b \right ) \ln \left (1+\sin \left (d x +c \right )\right )}{4 d}+\frac {3 b \sin \left (d x +c \right )}{2 d}+\frac {\left (a +b \sin \left (d x +c \right )\right ) \left (\tan ^{2}\left (d x +c \right )\right )}{2 d} \]
command
integrate((a+b*sin(d*x+c))*tan(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 \[ \text {Timed out} \]_______________________________________________________