\[ \int \tan ^8(c+d x) \, dx \]
Optimal antiderivative \[ x -\frac {\tan \left (d x +c \right )}{d}+\frac {\tan ^{3}\left (d x +c \right )}{3 d}-\frac {\tan ^{5}\left (d x +c \right )}{5 d}+\frac {\tan ^{7}\left (d x +c \right )}{7 d} \]
command
integrate(tan(d*x+c)^8,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 \[ \text {Exception raised: NotImplementedError} \]_______________________________________________________