\[ \int \cos (c+d x) (a+b \tan (c+d x))^3 \, dx \]
Optimal antiderivative \[ \frac {3 a \,b^{2} \arctanh \left (\sin \left (d x +c \right )\right )}{d}-\frac {\cos \left (d x +c \right ) \left (b -a \tan \left (d x +c \right )\right ) \left (a +b \tan \left (d x +c \right )\right )^{2}}{d}-\frac {b \sec \left (d x +c \right ) \left (2 a^{2}-2 b^{2}+a b \tan \left (d x +c \right )\right )}{d} \]
command
integrate(cos(d*x+c)*(a+b*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 \[ \text {Exception raised: NotImplementedError} \]_______________________________________________________