\[ \int \cos ^4(c+d x) (a+b \tan (c+d x))^2 \, dx \]
Optimal antiderivative \[ \frac {\left (3 a^{2}+b^{2}\right ) x}{8}-\frac {\left (\cos ^{4}\left (d x +c \right )\right ) \left (b -a \tan \left (d x +c \right )\right ) \left (a +b \tan \left (d x +c \right )\right )}{4 d}-\frac {\left (\cos ^{2}\left (d x +c \right )\right ) \left (2 a b -\left (3 a^{2}+b^{2}\right ) \tan \left (d x +c \right )\right )}{8 d} \]
command
integrate(cos(d*x+c)^4*(a+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 \[ \text {Exception raised: NotImplementedError} \]_______________________________________________________