\[ \int \frac {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+\left (6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-243 x^2-189 x^3-57 x^4-6 x^5\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+81 x+63 x^2+19 x^3+2 x^4\right ) \log ^3\left (\frac {e^2}{3 x}\right )}{-27 x^3-27 x^4-9 x^5-x^6+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-81 x^2-27 x^3-3 x^4\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+27 x+9 x^2+x^3\right ) \log ^3\left (\frac {e^2}{3 x}\right )} \, dx \]
Optimal antiderivative \[ x^{2}+\frac {x^{2}}{\left (3+x \right )^{2} \left (\ln \! \left (\frac {{\mathrm e}^{2}}{3 x}\right )-x \right )^{2}}+x +10 \]
command
Integrate[(6*x + 2*x^2 - 25*x^3 - 81*x^4 - 63*x^5 - 19*x^6 - 2*x^7 + (6*x + 81*x^2 + 243*x^3 + 189*x^4 + 57*x^5 + 6*x^6)*Log[E^2/(3*x)] + (-81*x - 243*x^2 - 189*x^3 - 57*x^4 - 6*x^5)*Log[E^2/(3*x)]^2 + (27 + 81*x + 63*x^2 + 19*x^3 + 2*x^4)*Log[E^2/(3*x)]^3)/(-27*x^3 - 27*x^4 - 9*x^5 - x^6 + (81*x^2 + 81*x^3 + 27*x^4 + 3*x^5)*Log[E^2/(3*x)] + (-81*x - 81*x^2 - 27*x^3 - 3*x^4)*Log[E^2/(3*x)]^2 + (27 + 27*x + 9*x^2 + x^3)*Log[E^2/(3*x)]^3),x]
Mathematica 13.1 output
\[ \int \frac {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+\left (6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-243 x^2-189 x^3-57 x^4-6 x^5\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+81 x+63 x^2+19 x^3+2 x^4\right ) \log ^3\left (\frac {e^2}{3 x}\right )}{-27 x^3-27 x^4-9 x^5-x^6+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-81 x^2-27 x^3-3 x^4\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+27 x+9 x^2+x^3\right ) \log ^3\left (\frac {e^2}{3 x}\right )} \, dx \]
Mathematica 12.3 output
\[ \text {output too large to display} \]