\[ \int \frac {-4096 x^3-768 x^6-48 x^9-x^{12}+\left (-73728+442368 x-516096 x^2-446976 x^3-18432 x^4-105984 x^5-82944 x^6-12096 x^7-7200 x^8-5184 x^9-864 x^{10}-162 x^{11}-108 x^{12}-18 x^{13}\right ) \log (x)+\left (73728-221184 x-202752 x^3-142848 x^4-13824 x^5-41472 x^6-17280 x^7-864 x^8-2592 x^9-864 x^{10}-54 x^{12}-18 x^{13}\right ) \log ^2(x)}{4096 x^3+768 x^6+48 x^9+x^{12}} \, dx \]
Optimal antiderivative \[ 3+{\mathrm e}^{5}-9 \left (x -\frac {1}{\frac {1}{16} x^{4}+x}+3\right )^{2} \ln \left (x \right )^{2}-x \]
command
Int[(-4096*x^3 - 768*x^6 - 48*x^9 - x^12 + (-73728 + 442368*x - 516096*x^2 - 446976*x^3 - 18432*x^4 - 105984*x^5 - 82944*x^6 - 12096*x^7 - 7200*x^8 - 5184*x^9 - 864*x^10 - 162*x^11 - 108*x^12 - 18*x^13)*Log[x] + (73728 - 221184*x - 202752*x^3 - 142848*x^4 - 13824*x^5 - 41472*x^6 - 17280*x^7 - 864*x^8 - 2592*x^9 - 864*x^10 - 54*x^12 - 18*x^13)*Log[x]^2)/(4096*x^3 + 768*x^6 + 48*x^9 + x^12),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \text {output too large to display} \]
Rubi 4.16.1 under Mathematica 13.3.1 output \[ \int \frac {-4096 x^3-768 x^6-48 x^9-x^{12}+\left (-73728+442368 x-516096 x^2-446976 x^3-18432 x^4-105984 x^5-82944 x^6-12096 x^7-7200 x^8-5184 x^9-864 x^{10}-162 x^{11}-108 x^{12}-18 x^{13}\right ) \log (x)+\left (73728-221184 x-202752 x^3-142848 x^4-13824 x^5-41472 x^6-17280 x^7-864 x^8-2592 x^9-864 x^{10}-54 x^{12}-18 x^{13}\right ) \log ^2(x)}{4096 x^3+768 x^6+48 x^9+x^{12}} \, dx \]__________________________________________