\[ \int \frac {24 x^2+8 x^4-2 x^6}{48+96 x^2+24 x^3+72 x^4+24 x^5+27 x^6+6 x^7+3 x^8} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{2}+\frac {2 x}{3 \left (x +\left (x +\frac {2}{x}\right )^{2}\right )}+\frac {4}{3}-2 \ln \! \left (5\right ) \]
command
Int[(24*x^2 + 8*x^4 - 2*x^6)/(48 + 96*x^2 + 24*x^3 + 72*x^4 + 24*x^5 + 27*x^6 + 6*x^7 + 3*x^8),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {24 x^2+8 x^4-2 x^6}{48+96 x^2+24 x^3+72 x^4+24 x^5+27 x^6+6 x^7+3 x^8} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {2 x^3}{3 \left (x^4+x^3+4 x^2+4\right )} \]