\[ \int \frac {e^x \left (-7+x+9 x^2+x^3-x^4\right )+e^x \left (7-9 x-2 x^2+x^3\right ) \log (x)}{49 x^2-14 x^3-13 x^4+2 x^5+x^6} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{x} \left (x -\ln \! \left (x \right )\right )}{x \left (x +8-\left (1+x \right )^{2}\right )} \]
command
Int[(E^x*(-7 + x + 9*x^2 + x^3 - x^4) + E^x*(7 - 9*x - 2*x^2 + x^3)*Log[x])/(49*x^2 - 14*x^3 - 13*x^4 + 2*x^5 + x^6),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^x \left (-7+x+9 x^2+x^3-x^4\right )+e^x \left (7-9 x-2 x^2+x^3\right ) \log (x)}{49 x^2-14 x^3-13 x^4+2 x^5+x^6} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \text {output too large to display} \]