\[ \int \frac {-40 x+60 x^5+\frac {\left (-10+15 x^4\right )^5 \left (-100 x-1350 x^5\right )}{e}}{-8+12 x^4+\frac {\left (-10+15 x^4\right )^5 \left (-40+60 x^4\right )}{e}+\frac {\left (-10+15 x^4\right )^{10} \left (-50+75 x^4\right )}{e^2}} \, dx \]
Optimal antiderivative \[ \frac {x^{2}}{{\mathrm e}^{5 \ln \left (15 x^{4}-10\right )-1}+\frac {2}{5}} \]
command
integrate(((-1350*x^5-100*x)*exp(5*log(15*x^4-10)-1)+60*x^5-40*x)/((75*x^4-50)*exp(5*log(15*x^4-10)-1)^2+(60*x^4-40)*exp(5*log(15*x^4-10)-1)+12*x^4-8),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {5 \, x^{2} e}{3796875 \, x^{20} - 12656250 \, x^{16} + 16875000 \, x^{12} - 11250000 \, x^{8} + 3750000 \, x^{4} + 2 \, e - 500000} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \mathit {undef} \]________________________________________________________________________________________