\[ \int \sin ^4(c+d x) (a+b \tan (c+d x))^2 \, dx \]
Optimal antiderivative \[ \frac {3 \left (a^{2}-5 b^{2}\right ) x}{8}-\frac {2 a b \ln \left (\cos \left (d x +c \right )\right )}{d}+\frac {b^{2} \tan \left (d x +c \right )}{d}+\frac {\left (\cos ^{2}\left (d x +c \right )\right ) \left (7 b -5 a \tan \left (d x +c \right )\right ) \left (a +b \tan \left (d x +c \right )\right )}{8 d}+\frac {\left (\cos ^{3}\left (d x +c \right )\right ) \sin \left (d x +c \right ) \left (a +b \tan \left (d x +c \right )\right )^{2}}{4 d} \]
command
integrate(sin(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 \[ \text {Exception raised: NotImplementedError} \]_______________________________________________________