\[ \int \frac {-5 x+25 x^2+5 e^4 x^2+20 x^3+45 x^4-30 x^5-10 x^6+5 x^7+\left (35+5 e^4+5 x+5 x^2-5 x^3-10 x^4+5 x^5\right ) \log \left (7+e^4+x+x^2-x^3-2 x^4+x^5\right )}{7 x^2+e^4 x^2+x^3+x^4-x^5-2 x^6+x^7} \, dx \]
Optimal antiderivative \[ 5 x -\frac {5 \ln \! \left (7+x \left (\left (-x^{2}+x +1\right )^{2}-x \right )+{\mathrm e}^{4}\right )}{x} \]
command
Int[(-5*x + 25*x^2 + 5*E^4*x^2 + 20*x^3 + 45*x^4 - 30*x^5 - 10*x^6 + 5*x^7 + (35 + 5*E^4 + 5*x + 5*x^2 - 5*x^3 - 10*x^4 + 5*x^5)*Log[7 + E^4 + x + x^2 - x^3 - 2*x^4 + x^5])/(7*x^2 + E^4*x^2 + x^3 + x^4 - x^5 - 2*x^6 + x^7),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {-5 x+25 x^2+5 e^4 x^2+20 x^3+45 x^4-30 x^5-10 x^6+5 x^7+\left (35+5 e^4+5 x+5 x^2-5 x^3-10 x^4+5 x^5\right ) \log \left (7+e^4+x+x^2-x^3-2 x^4+x^5\right )}{7 x^2+e^4 x^2+x^3+x^4-x^5-2 x^6+x^7} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ 5 x-\frac {5 \log \left (x^5-2 x^4-x^3+x^2+x+e^4+7\right )}{x} \]