\[ \int \frac {-9 x^4-2 x^5+e^{15} \left (288 x-152 x^2-48 x^3\right )+e^{20} \left (-148+184 x-33 x^2-18 x^3\right )+e^{10} \left (-215 x^2+6 x^3+12 x^4\right )+e^5 \left (72 x^3+16 x^4\right )}{-8 e^5 x^3+x^4+e^{20} \left (16-24 x+9 x^2\right )+e^{15} \left (-32 x+24 x^2\right )+e^{10} \left (24 x^2-6 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {x}{3 x -\left (x \,{\mathrm e}^{-5}-2\right )^{2}}+x -\left (5+x \right )^{2} \]
command
integrate(((-18*x^3-33*x^2+184*x-148)*exp(5)^4+(-48*x^3-152*x^2+288*x)*exp(5)^3+(12*x^4+6*x^3-215*x^2)*exp(5)^2+(16*x^4+72*x^3)*exp(5)-2*x^5-9*x^4)/((9*x^2-24*x+16)*exp(5)^4+(24*x^2-32*x)*exp(5)^3+(-6*x^3+24*x^2)*exp(5)^2-8*x^3*exp(5)+x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -x^{2} - 9 \, x - \frac {x e^{10}}{x^{2} - 3 \, x e^{10} - 4 \, x e^{5} + 4 \, e^{10}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {2 \, x^{5} + 9 \, x^{4} + {\left (18 \, x^{3} + 33 \, x^{2} - 184 \, x + 148\right )} e^{20} + 8 \, {\left (6 \, x^{3} + 19 \, x^{2} - 36 \, x\right )} e^{15} - {\left (12 \, x^{4} + 6 \, x^{3} - 215 \, x^{2}\right )} e^{10} - 8 \, {\left (2 \, x^{4} + 9 \, x^{3}\right )} e^{5}}{x^{4} - 8 \, x^{3} e^{5} + {\left (9 \, x^{2} - 24 \, x + 16\right )} e^{20} + 8 \, {\left (3 \, x^{2} - 4 \, x\right )} e^{15} - 6 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{10}}\,{d x} \]________________________________________________________________________________________