\[ \int \cos ^3(c+d x) (a \sin (c+d x)+b \tan (c+d x))^2 \, dx \]
Optimal antiderivative \[ \frac {a b x}{4}-\frac {a b \cos \left (d x +c \right ) \sin \left (d x +c \right )}{4 d}+\frac {\left (4 a^{2}+b^{2}\right ) \left (\sin ^{3}\left (d x +c \right )\right )}{30 d}+\frac {b \left (b +a \cos \left (d x +c \right )\right ) \left (\sin ^{3}\left (d x +c \right )\right )}{10 d}+\frac {\left (b +a \cos \left (d x +c \right )\right )^{2} \left (\sin ^{3}\left (d x +c \right )\right )}{5 d} \]
command
integrate(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,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 \[ \text {Timed out} \]_______________________________________________________