\[ \int \frac {150-30 e-225 x}{100 x^3+4 e^2 x^3-200 x^4+100 x^5+e \left (-40 x^3+40 x^4\right )} \, dx \]
Optimal antiderivative \[ 4+\frac {5}{\left (\frac {4 \,{\mathrm e}}{3}+\frac {20 x}{3}-\frac {20}{3}\right ) x^{2}} \]
command
integrate((-30*exp(1)-225*x+150)/(4*x^3*exp(1)^2+(40*x^4-40*x^3)*exp(1)+100*x^5-200*x^4+100*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {375}{4 \, {\left (5 \, x + e - 5\right )} {\left (e^{2} - 10 \, e + 25\right )}} - \frac {15 \, {\left (5 \, x - e + 5\right )}}{4 \, x^{2} {\left (e^{2} - 10 \, e + 25\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________