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