22.28 Problem number 5022

$$\int \frac{500-5x^2+125\log (3)+(-625-125\log (3))\log (x)+(-125+125\log (x))\log (\log (x))}{25x^2+10x^3+x^4+(-1250x-250x^2+(-250x-50x^2)\log (3))\log (x)+(15625+6250\log (3)+625{\log }^2(3)){\log }^2(x)+((250x+50x^2)\log (x)+(-6250-1250\log (3)){\log }^2(x))\log (\log (x))+625{\log }^2(x){\log }^2(\log (x))}dx$$

Optimal antiderivative $$\frac{x}{x(1+\frac{x}{5})+5(\ln \left(\ln \left(x\right)\right)-5-\ln \left(3\right))\ln \left(x\right)}$$

command

Integrate[(500 - 5*x^2 + 125*Log[3] + (-625 - 125*Log[3])*Log[x] + (-125 + 125*Log[x])*Log[Log[x]])/(25*x^2 + 10*x^3 + x^4 + (-1250*x - 250*x^2 + (-250*x - 50*x^2)*Log[3])*Log[x] + (15625 + 6250*Log[3] + 625*Log[3]^2)*Log[x]^2 + ((250*x + 50*x^2)*Log[x] + (-6250 - 1250*Log[3])*Log[x]^2)*Log[Log[x]] + 625*Log[x]^2*Log[Log[x]]^2),x]

Mathematica 13.1 output

$$\int \frac{500-5x^2+125\log (3)+(-625-125\log (3))\log (x)+(-125+125\log (x))\log (\log (x))}{25x^2+10x^3+x^4+(-1250x-250x^2+(-250x-50x^2)\log (3))\log (x)+(15625+6250\log (3)+625{\log }^2(3)){\log }^2(x)+((250x+50x^2)\log (x)+(-6250-1250\log (3)){\log }^2(x))\log (\log (x))+625{\log }^2(x){\log }^2(\log (x))}dx$$

Mathematica 12.3 output

$$\frac{5x}{x(5+x)+25\log (x)(-5+\log \left(\frac{\log (x)}{3}\right))}$$