\[ \int \frac {180+90 x^2+360 e x^2-90 e^6 x^2+30 x^3-90 e^2 x^3}{144+1152 x+2160 x^2+9 e^{20} x^2-600 x^3-60 x^4+12 x^5-144 e^3 x^5+x^6+9 e^4 x^6+e^{15} \left (-144 x^2+36 e x^3\right )+e^{10} \left (72 x+864 x^2-36 x^3-432 e x^3-6 x^4+54 e^2 x^4\right )+e \left (-576 x^2-2304 x^3+288 x^4+48 x^5\right )+e^2 \left (72 x^3+864 x^4-36 x^5-6 x^6\right )+e^5 \left (-576 x-2304 x^2+288 x^3+48 x^4-432 e^2 x^4+36 e^3 x^5+e \left (144 x^2+1728 x^3-72 x^4-12 x^5\right )\right )} \, dx \]
Optimal antiderivative \[ \frac {5}{\frac {4-\frac {x^{3}}{3}}{x}+\left ({\mathrm e}^{5}+{\mathrm e} x -4\right )^{2}-2 x} \]
command
integrate((-90*x^2*exp(1)*exp(5)-90*x^3*exp(1)^2+360*x^2*exp(1)+30*x^3+90*x^2+180)/(9*x^2*exp(5)^4+(36*x^3*exp(1)-144*x^2)*exp(5)^3+(54*x^4*exp(1)^2-432*x^3*exp(1)-6*x^4-36*x^3+864*x^2+72*x)*exp(5)^2+(36*x^5*exp(1)^3-432*x^4*exp(1)^2+(-12*x^5-72*x^4+1728*x^3+144*x^2)*exp(1)+48*x^4+288*x^3-2304*x^2-576*x)*exp(5)+9*x^6*exp(1)^4-144*x^5*exp(1)^3+(-6*x^6-36*x^5+864*x^4+72*x^3)*exp(1)^2+(48*x^5+288*x^4-2304*x^3-576*x^2)*exp(1)+x^6+12*x^5-60*x^4-600*x^3+2160*x^2+1152*x+144),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {15 \, x}{3 \, x^{3} e^{2} - x^{3} + 6 \, x^{2} e^{6} - 24 \, x^{2} e - 6 \, x^{2} + 3 \, x e^{10} - 24 \, x e^{5} + 48 \, x + 12} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________