\[ \int \frac {-5 x-4 x^2+x^3+e^{7+x} \left (4+3 x-x^2\right )+\left (-8-10 x+3 x^2+e^{7+x} \left (4 x+3 x^2-x^3\right )\right ) \log (x)+\left (-4-3 x+x^2\right ) \log (1+x)}{-4 x-3 x^2+x^3} \, dx \]
Optimal antiderivative \[ \ln \! \left (x \right ) \left (\ln \! \left (x \right )-{\mathrm e}^{x +7}+\ln \! \left (1+x \right )\right )+x -\ln \! \left (4-x \right ) \]
command
integrate(((x^2-3*x-4)*log(1+x)+((-x^3+3*x^2+4*x)*exp(x+7)+3*x^2-10*x-8)*log(x)+(-x^2+3*x+4)*exp(x+7)+x^3-4*x^2-5*x)/(x^3-3*x^2-4*x),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \text {could not integrate} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ -e^{\left (x + 7\right )} \log \left (x\right ) + \log \left (x + 1\right ) \log \left (x\right ) + \log \left (x\right )^{2} + x - \log \left (x - 4\right ) \]