\[ \int \left (a+b \tan ^3(c+d x)\right )^3 \, dx \]
Optimal antiderivative \[ a \left (a^{2}-3 b^{2}\right ) x +\frac {b \left (3 a^{2}-b^{2}\right ) \ln \left (\cos \left (d x +c \right )\right )}{d}+\frac {3 a \,b^{2} \tan \left (d x +c \right )}{d}+\frac {b \left (3 a^{2}-b^{2}\right ) \left (\tan ^{2}\left (d x +c \right )\right )}{2 d}-\frac {a \,b^{2} \left (\tan ^{3}\left (d x +c \right )\right )}{d}+\frac {b^{3} \left (\tan ^{4}\left (d x +c \right )\right )}{4 d}+\frac {3 a \,b^{2} \left (\tan ^{5}\left (d x +c \right )\right )}{5 d}-\frac {b^{3} \left (\tan ^{6}\left (d x +c \right )\right )}{6 d}+\frac {b^{3} \left (\tan ^{8}\left (d x +c \right )\right )}{8 d} \]
command
integrate((a+b*tan(d*x+c)^3)^3,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 \[ \text {Timed out} \]_______________________________________________________