\[ \int \frac {\left (-1+x^3-x^5-2 x^7\right )^{2/3} \left (1-x^3+x^5+2 x^7\right ) \left (-3+2 x^5+8 x^7\right )}{x^9} \, dx \]
Optimal antiderivative \[ \frac {3 \left (-2 x^{7}-x^{5}+x^{3}-1\right )^{\frac {8}{3}}}{8 x^{8}} \]
command
Int[((-1 + x^3 - x^5 - 2*x^7)^(2/3)*(1 - x^3 + x^5 + 2*x^7)*(-3 + 2*x^5 + 8*x^7))/x^9,x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {\left (-1+x^3-x^5-2 x^7\right )^{2/3} \left (1-x^3+x^5+2 x^7\right ) \left (-3+2 x^5+8 x^7\right )}{x^9} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {3 \left (-2 x^7-x^5+x^3-1\right )^{8/3}}{8 x^8} \]