\[ \int \frac {e^{\frac {1}{2} (-1-10 x)} (-17-85 x)+e^x \left (-3 x^2+e^{\frac {1}{2} (-1-10 x)} (3+18 x)\right )}{3 e^{-1-10 x}-6 e^{\frac {1}{2} (-1-10 x)} x+3 x^2} \, dx \]
Optimal antiderivative \[ \frac {x \left (\frac {17}{3}-{\mathrm e}^{x}\right )}{x -{\mathrm e}^{-5 x -\frac {1}{2}}} \]
command
integrate((((18*x+3)*exp(-5*x-1/2)-3*x^2)*exp(x)+(-85*x-17)*exp(-5*x-1/2))/(3*exp(-5*x-1/2)^2-6*x*exp(-5*x-1/2)+3*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {x e^{\left (6 \, x + \frac {1}{2}\right )}}{x e^{\left (5 \, x + \frac {1}{2}\right )} - 1} + \frac {170}{3 \, {\left ({\left (10 \, x + 1\right )} e^{\left (5 \, x + \frac {1}{2}\right )} - e^{\left (5 \, x + \frac {1}{2}\right )} - 10\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {3 \, {\left (x^{2} - {\left (6 \, x + 1\right )} e^{\left (-5 \, x - \frac {1}{2}\right )}\right )} e^{x} + 17 \, {\left (5 \, x + 1\right )} e^{\left (-5 \, x - \frac {1}{2}\right )}}{3 \, {\left (x^{2} - 2 \, x e^{\left (-5 \, x - \frac {1}{2}\right )} + e^{\left (-10 \, x - 1\right )}\right )}}\,{d x} \]________________________________________________________________________________________