22.52 Problem number 9617

$$\int \frac{(10+e^x(2-2x)+e^{x^2}(2-4x^2)+8\log (2))\log \left(\frac{4x}{5+e^x+e^{x^2}-3x+4\log (2)}\right)}{5x+e^{x}x+e^{x^2}x-3x^2+4x\log (2)}dx$$

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

command

Integrate[((10 + E^x*(2 - 2*x) + E^x^2*(2 - 4*x^2) + 8*Log[2])*Log[(4*x)/(5 + E^x + E^x^2 - 3*x + 4*Log[2])])/(5*x + E^x*x + E^x^2*x - 3*x^2 + 4*x*Log[2]),x]

Mathematica 13.1 output

$$\int \frac{(10+e^x(2-2x)+e^{x^2}(2-4x^2)+8\log (2))\log \left(\frac{4x}{5+e^x+e^{x^2}-3x+4\log (2)}\right)}{5x+e^{x}x+e^{x^2}x-3x^2+4x\log (2)}dx$$

Mathematica 12.3 output

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