25.5 Problem number 8528

\[ \int \frac {-3+x-3 x^2+2 x^3+e^3 (-1+2 x)+e^{2 x} \left (x+x^2\right )+e^x \left (-2 x+2 x^2+x^3+e^3 (1+x)\right )}{10+2 e^6-12 x+2 x^2+2 e^{2 x} x^2-4 x^3+2 x^4+e^3 \left (-4 x+4 x^2\right )+e^x \left (4 e^3 x-4 x^2+4 x^3\right )} \, dx \]

Optimal antiderivative \[ \frac {\ln \left (6 x -5-\left (x -\left (x +{\mathrm e}^{x}\right ) x -{\mathrm e}^{3}\right )^{2}\right )}{4} \]

command

Integrate[(-3 + x - 3*x^2 + 2*x^3 + E^3*(-1 + 2*x) + E^(2*x)*(x + x^2) + E^x*(-2*x + 2*x^2 + x^3 + E^3*(1 + x)))/(10 + 2*E^6 - 12*x + 2*x^2 + 2*E^(2*x)*x^2 - 4*x^3 + 2*x^4 + E^3*(-4*x + 4*x^2) + E^x*(4*E^3*x - 4*x^2 + 4*x^3)),x]

Mathematica 13.1 output

\[ \frac {1}{4} \log \left (5+e^6-6 x+2 e^{3+x} x+2 e^3 (-1+x) x+x^2+e^{2 x} x^2+2 e^x (-1+x) x^2-2 x^3+x^4\right ) \]

Mathematica 12.3 output

\[ \int \frac {-3+x-3 x^2+2 x^3+e^3 (-1+2 x)+e^{2 x} \left (x+x^2\right )+e^x \left (-2 x+2 x^2+x^3+e^3 (1+x)\right )}{10+2 e^6-12 x+2 x^2+2 e^{2 x} x^2-4 x^3+2 x^4+e^3 \left (-4 x+4 x^2\right )+e^x \left (4 e^3 x-4 x^2+4 x^3\right )} \, dx \]________________________________________________________________________________________