\[ \int (a+a \sin (c+d x))^4 \tan (c+d x) \, dx \]
Optimal antiderivative \[ -\frac {8 a^{4} \ln \left (1-\sin \left (d x +c \right )\right )}{d}-\frac {8 a^{4} \sin \left (d x +c \right )}{d}-\frac {7 a^{4} \left (\sin ^{2}\left (d x +c \right )\right )}{2 d}-\frac {4 a^{4} \left (\sin ^{3}\left (d x +c \right )\right )}{3 d}-\frac {a^{4} \left (\sin ^{4}\left (d x +c \right )\right )}{4 d} \]
command
integrate((a+a*sin(d*x+c))^4*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 \[ \text {Timed out} \]_______________________________________________________