\[ \int \frac {-32 x^3+e^x \left (3-3 x-80 x^2\right ) \log (2)-50 e^{2 x} x \log ^2(2)+e^{4 x} \left (-64 x^2-160 e^x x \log (2)-100 e^{2 x} \log ^2(2)\right )}{16 x^2+40 e^x x \log (2)+25 e^{2 x} \log ^2(2)} \, dx \]
Optimal antiderivative \[ 4-x^{2}-\frac {3}{\frac {1}{1+\frac {\ln \left (2\right ) {\mathrm e}^{x}}{x}}-5}-{\mathrm e}^{4 x} \]
command
Integrate[(-32*x^3 + E^x*(3 - 3*x - 80*x^2)*Log[2] - 50*E^(2*x)*x*Log[2]^2 + E^(4*x)*(-64*x^2 - 160*E^x*x*Log[2] - 100*E^(2*x)*Log[2]^2))/(16*x^2 + 40*E^x*x*Log[2] + 25*E^(2*x)*Log[2]^2),x]
Mathematica 13.1 output
\[ \int \frac {-32 x^3+e^x \left (3-3 x-80 x^2\right ) \log (2)-50 e^{2 x} x \log ^2(2)+e^{4 x} \left (-64 x^2-160 e^x x \log (2)-100 e^{2 x} \log ^2(2)\right )}{16 x^2+40 e^x x \log (2)+25 e^{2 x} \log ^2(2)} \, dx \]
Mathematica 12.3 output
\[ -\frac {125 e^{4 x} \log ^2(2) \log ^4(32)+125 x^2 \log ^2(2) \log ^4(32)-\frac {5 x \log (8) \log ^5(32)}{4 x+e^x \log (32)}+80 e^{2 x} \left (1-2 x+2 x^2\right ) \log ^2(32) \left (75 \log ^2(2)-20 \log (2) \log (32)+\log ^2(32)\right )-2560 e^x \left (-6+6 x-3 x^2+x^3\right ) \log (32) \left (50 \log ^2(2)-15 \log (2) \log (32)+\log ^2(32)\right )+1024 x^5 \left (125 \log ^2(2)-40 \log (2) \log (32)+3 \log ^2(32)\right )}{5 \log ^6(32)} \]