\[ \int \frac {-156-87 x-6 x^2+2 x^3+e \left (-6 x-105 x^2-24 x^3+4 x^4\right )+e^2 \left (-18 x^4+2 x^5\right )}{-171-99 x-8 x^2+2 x^3+e \left (-117 x^2-28 x^3+4 x^4\right )+e^2 \left (-20 x^4+2 x^5\right )} \, dx \]
Optimal antiderivative \[ x +\ln \left (\frac {1}{x +3+x^{2} {\mathrm e}}+\frac {2 x}{3}-\frac {20}{3}\right ) \]
command
integrate(((2*x^5-18*x^4)*exp(1)^2+(4*x^4-24*x^3-105*x^2-6*x)*exp(1)+2*x^3-6*x^2-87*x-156)/((2*x^5-20*x^4)*exp(1)^2+(4*x^4-28*x^3-117*x^2)*exp(1)+2*x^3-8*x^2-99*x-171),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x - \log \left (x^{2} e + x + 3\right ) + \log \left ({\left | 2 \, x^{3} e - 20 \, x^{2} e + 2 \, x^{2} - 14 \, x - 57 \right |}\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {2 \, x^{3} - 6 \, x^{2} + 2 \, {\left (x^{5} - 9 \, x^{4}\right )} e^{2} + {\left (4 \, x^{4} - 24 \, x^{3} - 105 \, x^{2} - 6 \, x\right )} e - 87 \, x - 156}{2 \, x^{3} - 8 \, x^{2} + 2 \, {\left (x^{5} - 10 \, x^{4}\right )} e^{2} + {\left (4 \, x^{4} - 28 \, x^{3} - 117 \, x^{2}\right )} e - 99 \, x - 171}\,{d x} \]________________________________________________________________________________________