\[ \int (a+a \sin (c+d x)) \tan ^3(c+d x) \, dx \]
Optimal antiderivative \[ \frac {5 a \ln \left (1-\sin \left (d x +c \right )\right )}{4 d}-\frac {a \ln \left (1+\sin \left (d x +c \right )\right )}{4 d}+\frac {a \sin \left (d x +c \right )}{d}+\frac {a^{2}}{2 d \left (a -a \sin \left (d x +c \right )\right )} \]
command
integrate((a+a*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 \[ \text {Timed out} \]_______________________________________________________