\[ \int \left (a+b \tan ^3(c+d x)\right )^4 \, dx \]
Optimal antiderivative \[ \left (a^{4}-6 a^{2} b^{2}+b^{4}\right ) x +\frac {4 a b \left (a^{2}-b^{2}\right ) \ln \left (\cos \left (d x +c \right )\right )}{d}+\frac {b^{2} \left (6 a^{2}-b^{2}\right ) \tan \left (d x +c \right )}{d}+\frac {2 a b \left (a^{2}-b^{2}\right ) \left (\tan ^{2}\left (d x +c \right )\right )}{d}-\frac {b^{2} \left (6 a^{2}-b^{2}\right ) \left (\tan ^{3}\left (d x +c \right )\right )}{3 d}+\frac {a \,b^{3} \left (\tan ^{4}\left (d x +c \right )\right )}{d}+\frac {b^{2} \left (6 a^{2}-b^{2}\right ) \left (\tan ^{5}\left (d x +c \right )\right )}{5 d}-\frac {2 a \,b^{3} \left (\tan ^{6}\left (d x +c \right )\right )}{3 d}+\frac {b^{4} \left (\tan ^{7}\left (d x +c \right )\right )}{7 d}+\frac {a \,b^{3} \left (\tan ^{8}\left (d x +c \right )\right )}{2 d}-\frac {b^{4} \left (\tan ^{9}\left (d x +c \right )\right )}{9 d}+\frac {b^{4} \left (\tan ^{11}\left (d x +c \right )\right )}{11 d} \]
command
integrate((a+b*tan(d*x+c)^3)^4,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 \[ \text {Timed out} \]_______________________________________________________