\[ \int \left (a+b \tan ^4(c+d x)\right )^4 \, dx \]
Optimal antiderivative \[ \left (a +b \right )^{4} x -\frac {b \left (2 a +b \right ) \left (2 a^{2}+2 a b +b^{2}\right ) \tan \left (d x +c \right )}{d}+\frac {b \left (2 a +b \right ) \left (2 a^{2}+2 a b +b^{2}\right ) \left (\tan ^{3}\left (d x +c \right )\right )}{3 d}-\frac {b^{2} \left (6 a^{2}+4 a b +b^{2}\right ) \left (\tan ^{5}\left (d x +c \right )\right )}{5 d}+\frac {b^{2} \left (6 a^{2}+4 a b +b^{2}\right ) \left (\tan ^{7}\left (d x +c \right )\right )}{7 d}-\frac {b^{3} \left (4 a +b \right ) \left (\tan ^{9}\left (d x +c \right )\right )}{9 d}+\frac {b^{3} \left (4 a +b \right ) \left (\tan ^{11}\left (d x +c \right )\right )}{11 d}-\frac {b^{4} \left (\tan ^{13}\left (d x +c \right )\right )}{13 d}+\frac {b^{4} \left (\tan ^{15}\left (d x +c \right )\right )}{15 d} \]
command
integrate((a+tan(d*x+c)^4*b)^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 \[ \text {Timed out} \]_______________________________________________________