\[ \int \frac {618-164770 x-24360 x^2-33206 x^3-4820 x^4-240 x^5-4 x^6+e^{15} \left (20 x+4 x^3\right )+e^{10} \left (-1212 x-60 x^2-240 x^3-12 x^4\right )+e^5 \left (-30+24480 x+2418 x^2+4860 x^3+480 x^4+12 x^5\right )}{-8000+e^{15}+e^{10} (-60-3 x)-1200 x-60 x^2-x^3+e^5 \left (1200+120 x+3 x^2\right )} \, dx \]
Optimal antiderivative \[ 3+\left (\frac {3}{20-{\mathrm e}^{5}+x}+x^{2}+5\right )^{2} \]
command
integrate(((4*x^3+20*x)*exp(5)^3+(-12*x^4-240*x^3-60*x^2-1212*x)*exp(5)^2+(12*x^5+480*x^4+4860*x^3+2418*x^2+24480*x-30)*exp(5)-4*x^6-240*x^5-4820*x^4-33206*x^3-24360*x^2-164770*x+618)/(exp(5)^3+(-3*x-60)*exp(5)^2+(3*x^2+120*x+1200)*exp(5)-x^3-60*x^2-1200*x-8000),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x^{4} + 10 \, x^{2} + 6 \, x + \frac {3 \, {\left (2 \, x e^{10} - 80 \, x e^{5} + 810 \, x - 2 \, e^{15} + 120 \, e^{10} - 2410 \, e^{5} + 16203\right )}}{{\left (x - e^{5} + 20\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {2 \, {\left (2 \, x^{6} + 120 \, x^{5} + 2410 \, x^{4} + 16603 \, x^{3} + 12180 \, x^{2} - 2 \, {\left (x^{3} + 5 \, x\right )} e^{15} + 6 \, {\left (x^{4} + 20 \, x^{3} + 5 \, x^{2} + 101 \, x\right )} e^{10} - 3 \, {\left (2 \, x^{5} + 80 \, x^{4} + 810 \, x^{3} + 403 \, x^{2} + 4080 \, x - 5\right )} e^{5} + 82385 \, x - 309\right )}}{x^{3} + 60 \, x^{2} + 3 \, {\left (x + 20\right )} e^{10} - 3 \, {\left (x^{2} + 40 \, x + 400\right )} e^{5} + 1200 \, x - e^{15} + 8000}\,{d x} \]________________________________________________________________________________________